Answer
$(x,y,z) = (6,15,-9)$
Work Step by Step
$l: (x,y,z) = (-1,-6,5)+n(1,3,-2)$
The x-coordinate of the line has this form: $-1+n$
The y-coordinate of the line has this form: $-6+3n$
The z-coordinate of the line has this form: $5-2n$
We can find the vale of $n$ such that these three coordinates satisfy the equation of the plane:
$2x+3y+z = 48$
$2(-1+n)+3(-6+3n)+(5-2n) = 48$
$-2+2n-18+9n+5-2n = 48$
$9n-15= 48$
$9n= 63$
$n = 7$
We can find the point of intersection:
$l: (x,y,z) = (-1,-6,5)+n(1,3,-2)$
$(x,y,z) = (-1,-6,5)+(7)(1,3,-2)$
$(x,y,z) = (-1+7,-6+21,5-14)$
$(x,y,z) = (6,15,-9)$
