A key concept you need to use here is symmetry, which is related to which carbon atoms are in the same chemical environment. Basically, for every unique environemnt, there will usually be a corresponding NMR peak (unless forbidden by some other rule).
A plain benzene molecule would have one peak, as shown in your lower diagram, because every carbon is in the same environment. Another way of looking at this is that the ring can be rotated onto itself by turning through 60 degrees (or has 3 mirror planes running through opposite vertices of the hexagon).
However, this is NOT true for molecule A, which has two different substituents on the ring (ethyl and chlorine). Does that mean each carbon in the ring has a unique environment? No - because there is a vertical mirror plane running through the molecule (ignoring the kink in the ethyl group - this doesn't matter). So, there are only 4 carbon atoms in the ring with unique environment.
Then, you need to consider the non-ring carbons. Chlorine obviously doesn't count, but there are two carbons in the ethyl group, both in different environments (one bonded directly to ring, one in the end group).
Therefore the total number of unique environments is 4+2 = 6.