Given:

△egh ~ △ikl, hf and lj are medians. he = 9, li = 6, hf = x+2, and lj = 2x−4

find:

hf

The fact that the largest triangles are similar and that HF and LJ are medians, we know that triangle HFE and triangle LJI are congruent.
Similarity allows us to set up proportions of congruent sides.
(Write these fractions vertically and solve.
9/6 = (x + 2)/(2x - 4)

9(2x - 4) = 6(x + 2)
18x - 36 = 6x + 12
-6x. -6x
12x - 36 = 12
+36. +36
12x = 48
x = 4 but WAIT! HF = x + 2 so 4 + 2 = 6