Answer: infinitely many
Explanation:
Just rearrange the second equation:
a(y - x + 6) = 0
y - x + 6 = 0
y - x = -6
x - y = 6
You have two equations that are identical. The number of (x,y) pairs satisfying "both" equations is just the number of pairs satisfying the first one. (Think about it, satisfying one is satisfying both.)
There are infinitely many (x,y) pairs satisfying x - y = 6, so answer is "infinitely many solutions."