Given, initially the velocity of man V_m1 = -8 j

When he doubles his speed,his final velocity V_m2 = -16 j. 

Velocity of wind = V_w

Let, V_wm1 = -a i

and V_wm2 = -b i+b j

V_wm1 =V_w - V_m1

V_w =V_m1 +V_wm1

V_w =-a i  -8 j .......(1)

V_wm2 = V_w -V_m2

=-a i  -8 j+16 j

V_wm2 =-a i  +8 j .......(2)

V_wm2=-a i  +8 j = -b i+b j

So, a=b=8

and,  V_w =V_wm2 +V_m2

= -8 i+8 j-16 j

= -8 i-8 j

and magnitude of V_w  is  = √(8)² +(8)²

= √128 km/hr

And wind or air is flowing from North-east to south east direction,as shown in figure.