Suggest that someone do something
Suggest is most commonly followed by a that-clause in which the subjunctive is used:
subject + suggest + (that*) + subject + subjunctive
Don’t let the word ‘subjunctive’ scare you! This is not a verb tense that you need to memorize. It is not used very often. All you need to remember is that the subjunctive is the same as the base form of the verb.