Типичная ловушка: suggest doing (не suggest to do)

Глагол suggest не сочетается с инфинитивом to do для выражения предложения/совета. Правильно:

suggest + V-ing: I suggest starting now.
suggest + (that) + подлежащее + base form (сослагат./subjunctive): I suggest (that) he start now. (в BrE часто: I suggest (that) he should start now.)
suggest + существительное/идею: She suggested a break.

Неправильно:

Один и тот же исполнитель (я предлагаю нам начать → мы же и начнём): → suggest + V-ing: We suggest meeting at 6.
Другой исполнитель (он должен сделать): → suggest (that) + he do … / he should do …: I suggest (that) he apologize. / … he should apologize.

В конструкции с (that) после suggest часто опускают that; глагол стоит в base form (без to, без -s): I suggest he go. — это норма.

suggest + V-ing: They suggested taking a taxi.
suggest + (that) + S + base form: The teacher suggested (that) we review the rules.
suggest + noun: He suggested a different plan.
passive: It was suggested that the meeting be moved.
wh-clause (что именно): Can you suggest where to eat? (здесь where to eat — от глагола suggest, но инфинитив в составе вопросительного оборота, не после suggest напрямую.)

recommend ведёт себя так же: recommend doing / recommend (that) she do; recommend to do (в общ. англ.).
propose: в значении «предложить (идею)» → как suggest (propose doing / propose that…).
offer ≠ suggest: offer = «предложить сделать/дать (самому)» → offer to do: He offered to help.

I suggest to change the topic. → I suggest changing the topic.
She suggested him to wait. → She suggested (that) he wait. / … he should wait.
The manager suggested to move the meeting. → The manager suggested moving the meeting. / … suggested (that) we move it.