we have that
A(-6,-5) and B (4,0)
we know that
AP:PB is 2:3
so
(2+3)=5
AP=2/5
PB=3/5
step 1
find the x coordinate of P
Px=Ax+AP*ABx
where
Ax is the x coordinate of A
AP is 2/5
ABx is the distance AB in the x coordinate
so
PX=[-6+(2/5)*(4+6)]------>Px=-2
step 2
find the y coordinate of P
Py=Ay+AP*ABy
where
Ay is the y coordinate of A
AP is 2/5
ABy is the distance AB in the y coordinate
so
Py=[-5+(2/5)*(0+5)]------>Py=-3
the point P is (-2,-3)
see the attached figure
