In the example sentence, a colon incorrectly introduces a list. The reason this colon usage is incorrect is that the colon does not follow a complete, grammatically correct independent clause. When used to introduce items in a list colons must come at the end of a independent clause that does not end in a verb. The best way to correct the sentence is simply to delete the colon.

Since the example sentence places a colon after a grammatically incomplete clause. "I love," is not a complete sentence as it lacks an object. The best way to correct the underlined portion above is, "I love ice cream, cookies, and cake, but I need to stop eating so much sugar or I'm going to have health issues."

Colons serve primarily two purposes. The first is to precede a list of three or more things in a sentence, and the second is to join two clauses of a sentence where the second clause explains, defines, or clarifies the first clause. For the first purpose, however, you should avoid using a colon after a verb or a preposition. The best way to correct the sentence above is to delete the colon since it follows a verb. 

Here, a colon is incorrectly placed in the middle of a clause. Colons must come at the end of an independent clause that does not end in a verb. Thus, in this case, the only correction would be to simply delete the colon, the rest of the sentence is correct as written.

In this sentence a colon is incorrectly placed after a verb. While colons are often used to introduce lists, they are not used to introduce every list. If the clause before the colon ends with a verb, then it is correct to use a comma, and not a colon to introduce the list.

The underlined portion of the sentence has a simple, but common, grammatical error. The form "it's" can only be used for the contraction of "it is," and not for the possesive of "it"; therefore, the correct answer is "its leaders."

The subject of the sentence, "Monarchs," is written in the underlined portion as a possessive noun. Problematically, the word is not possessing anything in the sentence, and is instead being used as a plural subject. The proper correction is to make the word a simple plural, making "Monarchs in the Middle Ages" the correct answer choice.

The use of "mans" in the sentence is actually the plural form without the proper use of the apostrophe to show a plural. The correct form is actually "man's," making "the man's motives," the best choice among the answers.

The use of "color's" indicates a possesive, which is not the correct usage in the construction of the sentence. The phrase each other means that the plural form should be used; therefore, "in distinguishing colors from each other," is the correct answer choice.

The form "Athlete's" is incorrect in the sentence because the construction, with a lack of articles preceeding it, indicates a plural form. "Athlete's" is the singular possesive form, but the sentence requires the plural possessive "Athletes'" and the singular "popularity."