First.....find the area of the triangle
S = semi-perimeter = (12 + 12 + 8) / 2 = 32 / 2 = 16
Area = sqrt [ 16 ( 16 -12)^2 ( 16 - 8) ] = 32sqrt(2)
radius of incircle = ( 2 * Area ) / ( perimeter) = ( 2 * 32 sqrt (2) ] / 32 = 2sqrt (2)
Here's the image :
