How many 4-digit integers greater than zero have 3 or 6 as the third digit and 3 as the first?

It should be pretty straightforward for you to narrow down the list of possibilities.

There are a lot of 4-digit integers greater than zero. I don't care to think about how many; we don't care about quite a lot of them.

First, look only at the group of integers of form 3xxx. Now you're down to a thousand. Still a lot.

The other condition limits the group to integers of form 3x3x or 3x6x.

If I work from right to left in either of those forms, I start by saying that there are ten possibilities for the rightmost 'x.' There are ten possibilities for the leftmost 'x' too, so I multiply by ten and get a hundred. Two forms, so two hundred.

The direction I work in doesn't really matter. So this generalizes to other kinds of permutation problem.