Paired conjunction

The reason you can't get it right is because the test has it wrong. The answer it wants is

you can help your community by either volunteer your time or donating money

It looks like it's not worried about capital letters or punctuation.

Volunteer is obviously incorrect: even the question has volunteering. The required answer has also lost the "if you are too busy" information.

I'd also prefer either to go before by. I think repeating by sounds better. However the other way isn't wrong.

You can help your community either by volunteering your time, or — if you are too busy — by donating money.

You can help your community by either volunteering your time or donating money if you are too busy to volunteer.

Computerised tests are generally poor, because there are always many ways of expressing something well, and most of them are better than what is actually expected. Especially here!