$$\begin{aligned} & A=\{(x, y) ; 2 x+3 y=23, x, y \in N\} \\ & A=\{(1,7),(4,5),(7,3),(10,1)\} \\ & B=\{x:(x, y) \in A\} \\ & B=\{1,4,7,10\} \end{aligned}$$

So, total number of one-one functions from A to B is $$4!=24$$