This is a little tough to visualize conceptually, but I'll do my best to explain it.
Imagine just the lower mass for a second, it will drop at twice the speed as the second pulley by just the way it's drawn out. Likewise the second mass would fall at half the rate as the other string if the other mass wasn't there.
Looking at the lower mass again. It's overall force would be ma = -T + mg. Because the tension and mass are opposing each other and it's dropping downwards. The higher mass should be -1/2(ma) = -2T + mg. Since the lower mass is dropping, then this one is raising upwards at half the rate, but also it has two tensions instead of one holding it up.
Now it's simply plugging each equation into each other. a = (-T + mg)/m
-(1/2)m((-T+mg)/m) = -2T + mg
3mg = 5T
T = 3/5 (10) = 6N
I wouldn't worry too much about this problem, as there are a lot of calculations, but as long as you get the concept you should be fine.