In your diagram, A represents dog lovers and B represents cat lovers.
A' means everything that is not in A.
The inverted U means intersection.
Hence \(A'\cap B\) means everything that is both not in A and is in B simultaneously. That is indicated by the shaded region in your diagram.
As for whether the numbers are correct, that will depend on the data specified for your problem. Your data suggests there are 8 people in total, 4 of whom love dogs but not cats, one who loves cats but not dogs and 3 who love both dogs and cats.