What are the limitations on the lengths of the sides of any triangle?
Look at different cases.
If the base is a 4 by 5 by 6 triangle, what size can the other faces be?
How many different tetrahedra can have as its base a 4 by 5 by 6 triangle?
Can you find 8 or more possible tetrahedra?
How will you know when you have them all?