Answer
$80$ Kilometers Per Hour, because you drive for twice as long at 60km/h as you do at 120 km/h, the 60km/h ends up counting twice as much when you average in regards to time.
Work Step by Step
Average speed is defined as total distance traveled divided by total time,
$\frac{Distance_{total}}{Time_{total}} $
Furthermore, Total distance will be equivalent to the time it takes to drive one way times the speed times two. We know the speeds, so we can input them to get the distance if we introduce an intermediate variable for the time driven one way.
$\frac{120Km/h*Time_{t}*2}{Time_{total}} $
Time total is not like distance, however. Because the speed changes time must also change for the trips. The first half of the trip at 120kmh takes $t$ time to complete, the second half at 60kmh must then take $2t$ time to complete. If we plug in values we can see this to be true, 120km at 120km/h takes 1 hour, 120km at 60km/h takes 2 hours. Therefore total time is 3t:
$\frac{120Kmh*Time_{t}*2}{Time_{t}*3} $
Simplifying our like terms we get:
$\frac{80Km/h*Time_{t}}{Time_{t}} $ -> $80km/h$
