The correct answers are: "Crew, you must prepare yourselves for hyper-sleep," the captain announced. The ship's artificial intelligence finally taught itself how to tell knock-knock jokes. The engineers prided themselves on fixing the warp drive with nothing but duct tape.

...prepare yourselves... is correct. Because "Crew" refers to multiple people, the plural form "yourselves" is used instead of the singular "yourself."

...taught itself... is correct. The singular, non-human subject ("artificial intelligence") matches with "itself."

...prided themselves... is correct. The plural subject ("engineers") matches with "themselves."

Incorrect options:

"...disguised theirselves..." is incorrect. "Theirselves" is not a real word; the correct plural reflexive pronoun is themselves.

"...protect ourself..." is incorrect. "We" is plural, so the reflexive pronoun must also be plural: ourselves.