Is It Okay?

....they think difficult." is a British usage and would sound odd to the American ear. How about you Ozzies?

Oristar, The sentence is correct as written.

Many students face problems when they have to study a subject (that) they think is difficult.

The "that" is implied and does not have to appear in the sentence to affect its structure.

Roberta, what I could not understand is the clause "(that) they think is difficult". I could not figure out how can "is" be put together with the verb "think". In my comprehension, "they think is difficult" is not acceptable. While the grammatically correct one seems like "they think to be difficult" or "they think being difficult". But the writings sound no good/redundant. If writing it as "they think difficult", yes it is terse, buy it sounds like British English, as joe Nation has indicated. Uh, how can I understand this clause?

Oristar, The "is" doesn't go with the verb "think." It goes with the noun "subject." It's the subject that is difficult.

Many students face problems when they have to study a subject (that) they think is difficult.

In this sentence, "they think" is a kind of parenthetical phrase and is not relevant to how the sentence is structured, although it is relevant to the meaning.

Many students face problems when they have to study a subject that is difficult.

Roberta, is the clause actually like this:

Many students face problems when they have to study a subject that (that they think) is difficult.

If so, it can be easily understood.
And then, finally we got:

Many students face problems when they have to study a subject they think is difficult.

Am I on the right track?

Yes, on the right track and chugging along. :-)