If (2, p) is the midpoint of the line segment joining the points A(6, −5) and B(−2, 11),

The given points are A(6, −5) and B(−2, 11).
Let (x, y) be the mid point of AB. Then:

$x=\frac{x_{1}+x_{2}}{2}, y=\frac{y_{1}+y_{2}}{2}$

$\Rightarrow x=\frac{6+(-2)}{2}, y=\frac{-5+11}{2}$

$\Rightarrow x=\frac{6-2}{2}, y=\frac{-5+11}{2}$

$\Rightarrow x=\frac{4}{2}, y=\frac{6}{2}$

$\Rightarrow x=2, y=3$

So, the midpoint of AB is (2, 3).
But it is given that the midpoint of AB is (2, p).
Therefore, the value of p = 3.