
One possible solution 
My last digit is 3 times my first digit:
This statement says alot. First, the last digit must be a multiple of 3,
so it is either 3, 6 or 9. Second, given the last digit, we know the first
digit must be 1, 2 or 3, respectiviely. Thus, the number is: 1_3, 2_6, or
3_9.
My first digit is twice my middle digit:
This statement says the first digit must be a multiple of 2, that is, the
first digit is even. This means of the three possibilities generated above,
only one can be used, namely, 2_6. Thus, the answer is 216.
Unless you allow 000 as a 3 digit number, there is only
one possible answer!
Another solution 
Above I assumed the the units digit was the 3rd digit. In this solution,
I will assume that units is 1st, tens is 2nd, and hundreds is 3rd.
My last digit is 3 times my first digit:
The possibilities now are: 3_1, 6_2, or 9_3. My
first digit is twice my middle digit: First digit ie even so the only
possibility from above is 6_2. Thus, the answer is 612. Again, a unique
answer, although different from solution 1 since assumed aÊreversed order
of digits.
Now I have a request for you: Please let me know if
you find another solution, or discover if there is a problem with the
wording of this question.
Paul 
