Select the noun clause to complete the sentence.

They would study (choose) during lunch.

Choices

How the electoral college works
And chat about the news
The history of aluminum foil
For tomorrow's math exam

Is it the last one?

a noun clause includes a verb, and is not an independent clause (making a compound sentence).

Otherwise it is just a phrase

Ok, so it is the first one since it starts with how?

Examples:

A person who trusts no one can't be trusted. (Jerome Blattner).
That he believes his own story is remarkable. (Jerome Blattner).
Ask your child what he wants for dinner only if he's buying...
He knows all about art, but he doesn't know what he likes...
It is even harder for the average ape...

What part of those sentences are the noun clauses?

Steve: yes

A person who trusts no one can't be trusted. (Jerome Blattner).
That he believes his own story is remarkable. (Jerome Blattner).
Ask your child what he wants for dinner only if he's buying...
He knows all about art, but he doesn't know what he likes...
It is even harder for the average ape... ???

Check out diagramming sentences. It will make this stuff very clear.

Thank you for your help and advice I will check that out

So... what's the answer?

To select the correct noun clause to complete the sentence, "They would study (choose) during lunch," we need to identify the phrase that can function as a noun and make sense in the context of studying during lunch.

Out of the given choices, the correct noun clause is "For tomorrow's math exam." This clause can serve as a reason or purpose for their studying during lunch.

it's "how the Electoral College works"