The triangle inequality requires that the sum of the shorter sides, a, b of a triangle be greater than the third side c.
This means that
a+b > c
If the third side is the longest, then a=6, b=9, and c<15
That makes 15 an impossible side.
If the third side x is less than 9, then
6+x<9, that makes
x<9-6=3.
That makes 2 an impossible side.
So the possible sides are 4,7,10,12,
