用法是對的
suggest doing sth建議做某事(動名詞作賓語)
suggest sb's doing sth(動名詞作賓語帶有自己的邏輯主語sb's:所有格+動名詞,叫動名詞的復合結構)
suggest sb doing sth(動名詞的復合結構作賓語時,可以用代詞賓格或名詞普通格代替)
例子:
I suggested his leaving soon.
=I suggested him leaving soon.
I suggested the boy's leaving soon.
=I suggested the boy leaving soon.