O'Neill worked as a merchant seaman before tuberculosis forced him to rest and educate himself. (1 point)

[Underlined: "to rest and educate himself"]

APrepositional
BParticipial
CGerund
DInfinitive (It's Infinitive)

Writing twelve one-act plays and two longer works kept him busy for two years. (1 point)

[Underlined: "Writing twelve one-act plays and two longer works"]

APrepositional
BParticipial
CGerund (It's Gerund)
DInfinitive

Falling into three main phrases, O'Neill's work grew stronger during his life. (1 point)

[Underlined: "Falling into three main phrases"]

APrepositional
BParticipial (It's participial)
CGerund
DInfinitive

The correct answer is D. infinitive.
Infinitives are relatively easy to spot - usually, their form is TO + verb. As you can see here, you have the phrase 'to rest and educate himself,' which is an infinitive phrase, because 'to rest' and 'to educate' are both infinitives.

9. The correct answer is C. gerund.
Gerunds have a specific form - they are usually verbs + -ing (e.g. writing). They are always used as nouns in a sentence, meaning they can function as subjects, objects, etc. in a sentence. Here, the gerund phrase is used as the subject.

10. The correct answer is B. participial.
Although participles and gerunds look the same (both have the following form: verb + -ing), the main difference between them is their function. Gerunds function as nouns in the sentence; on the other hand, participles are often used as either adjectives or adverbs.