Explanation:
these 2 parallel lines create similar triangles.
that mags they're is one common scaling factor for the side lengths bergen the 2 triangles.
and that means they must have the same ratio.
the large triangle has the side lengths
24 + 9 = 33
32 + x
the smaller triangle has the corresponding side lengths
24
32
so, the equal ratios are
24/33 = 32/(32+x)
24(32 + x) = 32×33
32 + x = 32×33/24 = 4×11 = 44
x = 44 - 32 = 12