distance=speed times time, so let t and 2.2-t be the times to and from work (2.2hr = 2hr 12min).
So if d is the distance, t=d/16 hr and 2.2-t=d/5 hr, so d=16t=5(2.2-t) km.
Therefore 16t=11-5t, 21t=11, t=11/21 hrs. d=16×11/21=176/21=8.38km (approx).
So the distance to work is about 8.38km.
16km/hr is about 10mph which is a rather fast walking pace, more like a running pace or cycling. It could be that 16km/hr should have been 6km/hr and the question has a more sensible solution:
t=d/6 hr and d=6t=5(2.2-t) km. So 6t+5t=11, 11t=11 and t=1hr, so d=6×1=6km. This makes more sense because he walks home from work only slightly slower than he walks to work. The walk home takes 1hr 12min compared to the 1hr walk to work.