that 用法錯誤問題

"suggest" can be followed by [verb-ing], ["that" clause] or [object].
Oxford dictionary:
- suggest doing something; e.g. I suggested going in my car.
- suggest that; e.g. I suggest (that) we go out to eat.
- suggest something (to somebody) ; e.g. May I suggest a white wine with this dish, Sir?

Both sentences below are correct:

Tom suggests giving money to people who lost their jobs. 建議他自己
= Tom suggests that he (should) give money to people who lost their jobs.

Tom suggests our giving money to people who lost their jobs. 建議我們
= Tom suggests that we give money to people who lost their jobs.

I think the following sentences may be better:
Tom suggests giving money to people who lost their jobs.
Tom suggests that (someone) give(s) money to people who lost their jobs.