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Because $(6,6)$ is on the line, we have the slope $\frac{6-0}{6-b}=\frac{6-2a}{6-a}$, which simplifies to $3a+3b=ab$. We already know that's $48$ so $a+b=16, ab=48$, and thus $\lbrace a,b\rbrace=\lbrace4,12\rbrace$. This gives two possibilities for where $A$ and $B$ are; finding the respective equations of the line is then easy using one of the other points on the line.