Verified answer

[(x^2 - 4) / (24x)] / [(2 - x) / (8xy)] =

[(x^2 - 4) / (24x)] * [(8xy) / (2 - x)] =

[(x - 2)(x + 2)(8xy)] / [24x(2 - x)] =

-(x + 2)y / [3]

(note that (x - 2) / (2 - x) = -1 and

8xy / (24x) = y / 3

so this whole things simplifies to -y(x + 2) / 3