I suggest that he go/goes?

Question

I suggest that he go to the doctor as soon as he returns from taking examination.

Book says because the sentence involves suggestion so there should be go instead of goes. What kind of rule is this?

Answer 1

The rule is, 'go' in your sentence is a present subjunctive form.

There are several possibilities for this sentence:

I suggest that he go. (Present Subjunctive. More common in American English. Not very common in British English).
I suggest that he goes. (Present Indicative. Quite common in British English).
I suggest that he should go.

Answer 2

The original sentence needs to be streamlined, the clause “as soon as he returns from taking examination” is awkward sounding and filled with redundancies, it's also missing the definite article "the".

I suggest that he visit the doctor as soon as the examination finishes.

People do say they ‘go to’ and ‘see’ the doctor, but in a formal statement, which the OP appears to be striving for, replacing the verb go with visit makes it sound a tad more formal.

As for the subjunctive, it is used far more commonly in the US than in the UK, at least that's what everyone says on ELL and EL&U, see below [emphasis mine]

…when we come to the third person singular in the present tense, I understand that American English distinguishes between the mandative subjunctive ('She suggested that he go to the cinema') and the indicative ('She suggested that he goes to the cinema') to express the two meanings.
@Barrie England

and

This is an example of a subjunctive. The subjunctive form of the verb is frequently used in mandative clauses (certain clauses which contain the content of an order, desire, suggestion). The subjunctive uses the plain form of the verb. The same form as the bare infinitive. The Original Poster's example ‘I be’ would be grammatical in the following sentences:

• He demanded I be taken out and flogged.
• He suggested I be there before the proceedings commenced.
• It is essential that I be kept informed of any new developments.

The subjunctive is used more frequently in American English than in British, although it is perfectly normal in both.
@araucaria

A British person might well avoid the entire issue and say

He should go to the doctor.
He ought to visit/see the doctor as soon as possible.
He needs to see/go to the doctor's as soon as possible.