suggest/suggested (+ possessive adjective) + gerund:
He suggests going to Glastonbury
He suggested going to Glastonbury
He suggested/suggests my going to Glastonbury
suggest/suggested + that-clause (where both that and should may be omitted):
He suggests that I should go to Glastonbury
He suggested that I should go to Glastonbury
He suggested/suggests I should go to Glastonbury
He suggested/suggests I go to Glastonbury
He suggested I went to Glastonbury.
suggest/suggested + question word + infinitive:
He suggested where to go.
I suggested him to fix...
Hope this helps you understand the correct usage of the verb "suggest". Now you should be able to answer your question on your own. Try correcting your sentences. We are here for further help.
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