jmc

From the information given, we can construct the following equation: $xy+1=(x-4)(2y-1)$. This simplifies to $xy-x-8y=-3$. We can then apply Simon's Favorite Factoring Trick and add $8$ to both sides to get $xy-x-8y+8=5$. This can be factored into $$(x-8)(y-1)=5$$Since $x\le 10$, $x=9$ and $y=6$. Thus, the product of my two numbers is $9\cdot 6=\boxed{54}$.