in a traingle XYZ A is the mid point of XY and AB//XZ. is XZ is 8.4 cm . find the length of AB

You have similar triangles.

Since XA = AY
AY : XY = 1 : 2

triangle XYZ is similar to triangle AYB
XZ/XY = AB/AY
8.4/2 = AB/1
AB = 8.4/2 = 4.2