"quite a..." or "a quite..."

You’ve been having QUITE A long chat with the doctor.
This is A QUITE comfortable house.

These two sentences are both right.Is there any difference between “quite a…” and “a quite…”?
Here is an exercise:
–English is ________ difficult subject. I even want to drop it.
–You’d better not. I’ll help you ______ it.
A. quite a, with B. a quite, with
C. a very, for D. very a, with

Is B also right?

Yes, you can say:
English is a quite difficult subject, meaning that it’s very difficult.

.
You can also say “English is quite a difficult subject”.
I’d also say that word order (quite a) would be the more commonly used one.
.

English is ________ difficult subject. I even want to drop it.

i think the option “quite a” is correct.

And the BYU Corpus of American English would agree with you:

quite a + adj - 1213 per 1 million words
a quite + adj - 356 per 1 million words

It may be of interest to note that the former appears quite a lot in the Spoken register and the latter more in the Academic register.