Iam a number less than 40,000. all my digits are multiples of 3. my first, third, and fifth digits are the same. both my thousands digits and my tens digit are six more than the others.

The answer is 39,393.

This is because their are five spots:

_ _ _ _ _

If the first third and fifth are multiples of three here are some possible values
3,6,9

But since it is less than 40,000
the answer can only be 3, b/c 6 is greater than 4 and so is 9.  The numbers cant be more than single digit multiples or else the number would be much bigger than 40,000.

SO FAR...

3 _ 3 _ 3

 Now that you know those digits are 3, the second part says the remaining digits are 6 more than the one figured out.  So six more than 3 is 9.  Filling in the numerals for the final number, it comes out to be 39393. 

16 minutes is correct