I suggest that he study/studied medicine.
Suggest is the present form of verb. So according to it, the sentence should have study rather than studied. Studied is basically past form of the verb.
But the answer is studied. Any rules regarding this?
Assuming the sense of the sentence is that you are giving advice to the person as to what to study, then "I suggest that he study medicine" is correct.
The sentence "I suggest that he studied medicine", to me, conveys a sense of a group of people speculating about what the person "he" refers to studied in the past, and that "I" am putting forward a guess that it was medicine.
I'm afraid, which book says it's 'studied'?
You are using the present tense i.e. 'suggest'. The word 'study' cannot be in the past then.
I suggest that he
If you want to talk about the past tense, the advisory verb suggest will take 'should'
I suggested that he should study medicine.