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.
沒有區別，可以互換。
suggest（that）sb (should) do sth建議某人做某事
Tom suggested（that）she (should) go to see a doctor.湯姆建議她應該去看醫生。
suggest one's doing sth建議某人做某事
I suggest your opening the windows.我建議你打開窗戶。
詞義辨析
re買粉絲mend，advocate，propose，suggest，prescribe這些動詞均含“勸告、主張、建議”之意。
re買粉絲mend指向對方提出公開的建議或規勸。
advocate指公開表明對某事或某行為的完全贊同，語氣強于re買粉絲mend。
propose多指較正式地提出建議。
suggest語氣較委婉，指提出不成熟的建議或參見意見。
prescribe多指醫生開處方。