For the mean let's finish this off
First off you do the following for each column multiply the number of families by the number of children. Remember sigma notation is applied. So thus,
k times 0 you know what that is, 0.
2 families with one child, that is just 2 times 1
9 families with 2 children, that is 9 times 2
6 families with 3 children, that is 6 times 3
7 families with 4 children, that is 7 times 4.
Now luckily k is 0 otherwise this would be an interesting question. Here this becomes 2+18+18+28+0=66. We are given the mean is 2 so therefore we have the total number of families and children which is 66 now this question is basically,66/k+2+9+6+7=2, here we swap the k+2+9+6+7 term with 2 and here we should see that 33=k+2+9+6+7. To find k very simple, k=33-2-9-6-7=9.