And -- The Greek word translated as "and" is used as the conjunction "and", but it also is used to add emphasis ("also").

that -- (IW) There is no Greek word "that" here. It is added to make this sound like a paraphrase following a direct quote. However, if the previous verse is read as a direct quote, this one  should be to since it continues that statement. 

repentance -- "Repentance," is the uncommon noun form of a very common verb. It means "a change of mind or heart", "repentance", "regret", "afterthought", and "correction". In English, this idea is can be expressed as "hindsight". It is from a verb that means "to perceive afterward".  Though in the form of an object, this word is not exactly the object of the verb "preach" because that word is passive (see below).

and -- (WW) There is no "and" here. Instead there is a preposition that means The word means "into" a place, "towards" as a direction, "in regards to" a subject, and "up to" limits in time and measure. The meaning here is clearly "in regards to". This word doesn't mean "and."  

remission -- (CW) "Remission" is the noun that means "letting go," "release," "relaxation," "exhaustion," "liberty," "exemption from attendance," "leave of absence," "divorce," and "the beginning [of anything]." It is the noun form of the word usually translated as "forgive" in the NT that has a meaning closer to "let go."  See this article for more. 

of -- This word "of"  comes from the possessive form (genitive case) of the following word that requires the addition of a preposition in English.  The most common is the "of" of possession.

sins  -- -- (CW) The word translated as "sins" means "missing the mark," "failure," "fault," and "error." Only in religious uses does it become "guilt" and "sin," having no sense of doing malicious evil in Greek. The best English translation is "mistake," "fault," or "failure" rather than what we commonly think of as the evils of "sin." See this article for more information and context. 

should -- (WF) This helping verb in English comes from the form of the Greek verb that indicates a possibility. We would usually say "might" or "should" in English, but this verb is not in that form.   

be -- This helping verb "be" indicates that the verb is passive. Helping or auxiliary verbs are needed to translate the Greek verb forms into English.

preached -- (CW, WF) The word translated as "preached" means "to act as a herald", "to proclaim," and "to declare."  It is not an active verb, but an infinitive, the third infinitive of the sentence, the first two were in the previous verse. The form is passive so "to be a herald" is the direct meaning. The word "preached" has a religious meaning that the Greek word didn't have. This is not an active verb but an infinitive.  

 in -- The word translated as "in" means "on", "over", "upon", "against", "before", "after", "during", "by" or "on." 

his -- The word translated as "his" is the Greek word commonly translated as third-person pronouns in English.  If this is a paraphrase, it would seem to refer to Jesus, but if it was a direct statement, it would refer to the Father.

missing "the/this"  -- (MW) The untranslated word is the Greek definite article," the," which usually precedes a noun or changes the word it precedes (adjective, infinitive, participle, etc.) to act like a noun. The Greek article is much closer to our demonstrative pronouns ("this," "that," "these," and "those"). See this article for more. 

name  -- The Greek word translated as "name" is much more complicated than it might at first appear. It can simply mean a "name" as in English, this can be many things. It doesn't mean the thing itself, but what people call it. For example, it can mean a "false name," or "a pretense" as we say "this is a marriage in name only." It can also mean representing another person's authority, as we say, "he is acting in the name of the boss."

among  -- The word translated as "among" means "into" a place, "towards" as a direction, "in regards to" a subject, and "up to" limits in time and measure.

all  -- The word translated as "all" is the Greek adjective meaning "all", "the whole", "every," and similar ideas. When it is used as a noun, we would say "everything." As an adverb, it means "in every way", "on every side," and "altogether."

missing "the/this"  -- (MW) The untranslated word is the Greek definite article," the," which usually precedes a noun or changes the word it precedes (adjective, infinitive, participle, etc.) to act like a noun. The Greek article is much closer to our demonstrative pronouns ("this," "that," "these," and "those"). See this article for more. 

nations -- The word translated as "nations" is usually translated as "gentiles" but it means "a group of people living together," a nation, a tribe, or a cast of people. Later it came to mean "barbarous nations" similar to our idea of ethnic people. It is in the same form as the "them" above, so "to them" or "for them." It is the Greek word from which we get our word "ethnic".

beginning -- "Beginning" is from a verb in the form of an adjective that means "to be first", "to begin," and "to make a beginning", "to rule", "to govern," and "to command."  The two meanings, "to start" and "to command" create different meanings when paired with the following verbs.  The form is that of an adjective, "beginning" or "starting".

at  -- The word translated as "at" means "from" in both location and when referring to a source. It does not mean "at".

Jerusalem -- The word "Jerusalem" denotes the city or its inhabitants. Two different forms of this word appear in the NT. This is the only time this form is used in Matthew. It is only used once in Mark, but not in Christ's words. It isn't used at all in John. This version is used most heavily in Luke, mostly in his narration, but a few times in Christ's words. It seems to be the more formally Greek version of the name.