how to use the verb "suggest"?
Should I say: What did he suggest you to do? or maybe " What did he suggest you do?

Question

Answer

The second one is correct. "What did he suggest you do?"

Answer

Of the two sentences in your question, Jerome's answer is correct; the usage rules that Aredin stated are also correct.

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Teacher had taught me 2 ways to use suggest :
S + suggest + Ving/N
S + suggest + where/what/when/which/how + to + V