The sentence can be divided as follows:

[After the commercial aired], [the model] [gained world-wide recognition and praise [from several top fashion magazines.]

[After the commercial aired]: Prepositional phrase

[the model]: the subject, who the action happens to!

[gained world-wide recognition and praise from several top fashion magazines.]: Predicate, with "gained" acting as the verb and "from several top fashion magazines" acting as a prepositional phrase.

"Model" is therefore the subject.

John is the subject of the sentence because he is the one who "liked to greet every student in his class by name." While "he" may look like a potentially correct answer, the phrase "Though he couldn't always do so" is an introductory phrase that is not grammatically a part of the main sentence. Because it could be omitted and the sentence would retain its same meaning, "he" cannot be the subject, because if you take away the subject of a declarative sentence, it cannot be a complete declarative sentence any more.

The subject of a sentence tells you who or what performs the action of the sentence.

Break down the sentence to see beyond any descriptive phrases and identify the simple subject and predicate:

Unfortunately, [Erin’s favorite vintage record] [broke in half during the moving process.]

Subject: "record"
Verb: "broke"

The subject of this sentence is therefore "record."

Tip: Don't be confused by the word "Erin's" just because a name is being used. A possessive name like this one that shows ownership is an adjective, not a noun, and cannot be the subject.

The subject of the sentence is what the sentence is about—the "who" or "what" that is actually performing the action. Breaking down the sentence may help you identify that James is the subject:

[After finally accepting an offer to attend his dream university], [James was finally able to relax and enjoy his last month of school.] 

The first dependent clause is a prepositional phrase, so you will not find the subject of the sentence there. If you focus on the rest of the sentence, you can break it down easily into [Subject] [Predicate]:

[James] [was finally able to relax and enjoy his last month of school.]

A sentence can be divided into its subject and its predicate. The subject is the "who" or "what" that performs the sentence's action.

Break down the sentence to see beyond any descriptive phrases and find the simple subject and predicate:

[The leather-bound, antique novel], (given to me by my mother for my college graduation), [remained on my nightstand for years as a reminder of home.]

The simple subject is "novel," and simple predicate is "remained," so "novel" is the subject of this sentence.

The subject of a sentence tells you who or what performs the action of the sentence.  

Try to look past the descriptive words and phrases in the sentence to find the simple subject and the simple predicate:

(Even after the streak of intense rainstorms), [my father’s rusty old truck] [could handle the muddy roads easily.]

Simple subject: "truck"
Simple predicate: "could handle"

The simple subject is "truck."

The subject of a sentence tells you who or what performs the action of the sentence or who or what the sentence is about.

The beginning of this sentence is just a description: "Tall, blonde, and radiently charismatic." The subject won't be found there. If we remove that part of the sentence, we're left with the following:

[Shelly] [was first in line to become head cheerleader.]

Subject: Shelly
Verb: was

This sentence is about Shelly, so she is the subject. We can also tell that she is the subject because the verb "was" describes her.

The subject of a sentence tells you who or what performs the action of the sentence or who or what the sentence is about.

Break down the sentence to see beyond any descriptive phrases and identify the simple subject and predicate:

[The sweet buttercream frosting] [cost Michelle extra but was most certainly worth the expense.]

The subject of the sentence is "frosting."

Do not be confused by the name Michelle; if a name is used in a sentence, it is not always the subject!

Although this sentence includes many different nouns, its main subject is "villagers" because they are the ones who are doing the main activity ("came to terms"). While "military" and "town" might each look like a potentially correct answer because they are the nouns one encounters in the sentence's first phrase, they are each contained within a prepositional phrase ("After the military left the town"), so neither can be the subject of the sentence. Similarly, "destruction" and "the soldiers" also appear within a prepositional phrase, "of the destruction the soldiers left in their wake," so neither of those nouns can be the subject either.

The subject is the part of the sentence that does the action. "Verbs" is the correct answer.