|x|+2|y|+|z|=4
for |y|=0, |x|+|z|=4 so 4n=4 * 4=16 cases
for |y|=1, y=+-1 and |x|+|z|=2 so 2 * 4 * 2=16 cases
for |y|=2 y=+-2 |x|+|z|=0 so 2 * 1 = 2 cases
so 16+16+2 = 34 integer solutions.

Each angle is 180(p-2)/p.
180-{360}/{p} = k
So 360/p has to be an integer.
360 = 2^3 * 3^2 * 5^1
So there are 4 * 3 * 2 = 24 possibilities, but we exclude 1 and 2, because p > = 3
So , 24 -2 = 22
Hence, choice (c) is the right answer