The solution of  $4x+\frac{6}{y}=15,6x-\frac{8}{y}=14$  lies on $y=px-2$ , then $p=$

$4xy+6=15y$ 

$4xy-15y=-6\to \left(1\right)$

$6xy-8=14y$

$6xy-14y=8$

$3xy-7y=4\to \left(2\right)$

Solve (1) and (2)

$4xy-15y=-6\to \left(1\right)\times \left(3\right)$

$3xy-7y=4\to \left(2\right)\times 4$

$y=2$

The value of $y=2$  in equation (1)

$4x\left(2\right)-15\left(2\right)=-6$

$8x-30=-6$

$8x=24$

$\therefore x=3$

$y=px-2$

$2=p\left(3\right)-2$

$\frac{4}{3}=p$

$\therefore p=\frac{4}{3}$