Suggest or suggest that
The verb suggest cannot be followed by object + infinitive. That-clauses and –ing forms are common.
Father suggested consulting a doctor. OR Father suggested that I should consult a doctor. (NOT Father suggested to consult a doctor.) (NOT Father suggested me to consult a doctor.)
Verb forms in that-clauses after suggest
In that-clauses after suggest, various verb forms are possible.
In British English, should + infinitive is common.
She suggested that I should get a job.
She suggests that I should get a job.
In American English, should + infinitive is rare. Instead Americans use a special verb form called subjunctive.
She suggested that I get a good job.
She suggests that I get a good job.
I suggested that he hire an attorney.
I suggest that he hire an attorney.
In British English, ordinary present and past tense forms are also possible.
She suggested that I got a degree in physics.
She suggests that I get a degree in physics.
I suggested that he consulted an attorney.
I suggest that he consults an attorney.
Suggest can be followed by a direct object.
What shall we eat? I suggest fish.
Suggest cannot be followed by an indirect object without a preposition.
Can you suggest a nice restaurant to me? (NOT Can you suggest me a nice restaurant?)