In order to calculate the age of the father, you first consider that the average of the family is 30, then, you have:
(x1 + x2 + x3 + x4 + x5 + x6)/6 = 30
where x3, x4, x5 and x6 are the ages of the children, x1 is the age of the mother and x2 is the age of the father
You cn write the previous expression as:
(x1 + x2)/7 + (x3+x4+x5+x6)/7 = 30
The second term in the second expression is the average age of the children, which is 12. Furthermore, the mother is 4 years younger than the father, that is, x1 = x2 - 4. You replace this values in the expression above and you obtain:
(x1 + x2)/7 + (x3+x4+x5+x6)/7 = 30
(x2 - 4 + x2)/7 + 12 = 30
Next, you solve for x2:
(x2 - 4 + x2)/7 + 12 = 30
(2x2 - 4)/7 + 12 = 30
multiply the previous expression by 7:
2x2 - 4 + 12(7) = 30(7)
2x2 - 4 + 84 = 210
2x2 = 130
x2 = 65
Then, the age of the father is 65