$$\begin{gathered} \text{ Matrix }A\text{ has }x\text{ rows and }x+4\text{ columns and another matrix }B\text{ has }y\text{ rows} \\ \text{and }2y-10 \text{ columns. Both }AB\text{ and }BA\text{ exist then }x\text{ and }y\text{ are } \end{gathered}$$

$$\begin{gathered} \text{ Matrix }A\text{ has }x\text{ rows and }x+4\text{ columns and another matrix }B\text{ has }y\text{ rows} \\ \text{and }2y-10 \text{ columns. Both }AB\text{ and }BA\text{ exist then }x\text{ and }y\text{ are } \end{gathered}$$
∴ number of columns of A is equal to number of rows of B,

⟹x+4=y,
and also number of columns of B is equal to number of rows of A,

⟹x=2y-10,
Solving both equations x=2, y=6