The correct option is B (5,6)
Let (h,k) be the mid point.
Equation of chord with a mid point is T=S1
⇒yk−4(x+h)=k2−8h⇒ky−4x=k2−4h
This line is identical with given line 2x−3y+8=0
Comparing both the lines, we get
k−3=−42=k2−4h−8
⇒k=6
and 16=k2−4h⇒h=5
Hence required mid point is (5,6)