2020/029) Solve in positive integers $ab - 4a -4b = -8$

Because it is symmetric in a ,b without loss of generality we can take $a>b$ and find a solution for the same
then permutation shall be another solution.

We need to factor the same in some form and as it is of the form $ab-4a-4b$ this shall have the form $(a-4)(b-4)$
Now $(a-4)(b-4) = ab -4a -4b + 16$
Or $(a-4)(b-4) = -8 + 16$ Putting the value of ab-4a-4b from given condition
Or $(a-4)(b-4) = 8$
For a and b to be integers we need to take the factors of 8 giving 2 sets 8 = 8 * 1 or 4 * 2
$a-4=8,b=4=>a=12, b= 5$

and
$a-4=4,b=2=>a=8, b= 6$