A man goes from a to b at v1 speed and  returns from b to a at v2 speed.

Let distance between a and b = d

let time taken by man go from a to b = t1 and time taken by man return from b to a =t2

As we know,

time = distance / speed

so, t1 = d /v1   and  t2= d/v2

ATQ,

average speed = total distance/total time

= (d+d) / (t1+t2 )

= (d+d) /(d/v1 + d/v2)

= 2d / (d(v2+v1)/v1*v2)

= (2v1*v2) / (v2+v1)

Answer = 2(v1*v2) / (v2+v1)