The mean of 4 numbers is 5 and the mean of 3 different numbers is...

The mean of a set of numbers is the sum of the numbers over the count of the set (the number of values).
We have a set of four numbers and the mean is 5. We can see that the sum of the values is 20:
$\frac{20}{4}=5$
We have another set of three numbers whose mean is 12. We can write that as:
$\frac{36}{3}=12$
To find the mean of the seven numbers together, we can add the values together and divide by 7:
$\frac{20+36}{7}=\frac{56}{7}=8$$\frac{20+36}{7}=\frac{56}{7}=8$