This sounds like a permutation question - basically how many combinations can you make with the following numbers. In this case we have 3 different variables which we're going to arrange into as many combinations as we can.
I like using the method described in the link below. Basically you figure out how many options you have in each "space" allowed in the number. In this case we have 3 "spaces" available in our 3 digit number:
You can look at the number we're looking for like this:
_#1_ _#2_ _#3_
In the #1 slot we can use any of the numbers allowed (2, 3 or 4), so we have 3 options here.
In the #2 slot we can only use the numbers not used in #1 slot (so if we used "2" in the #1 slot, we can only use "3" or "4" this time. So there are only 2 options here.
In the #3 slot we can only use the final number remaining. If we used "2" in #1 slot and "3" in #2 slot, we have to use "4" in the #3 slot, so we only have 1 option here.
When we multiply our options (3 x 2 x 1) we come up with 6 available numbers we can make using the 3 numbers supplied.