The vertex of parabola C is at the origin, the focus F coincides with the right focus of hyperbola x23-y26= 1, and a straight line L with a slope of 1 intersects parabola C.

∵ The focus f coincides with the right focus of the hyperbola x23-y26= 1

∴F(3,0)，

∴p2=3，

∴p=6，

The parabolic equation is y2 = 12x.

Let A(x 1, y 1) and B(x2, y2).

The equation of a straight line L with a slope of 1 passing through point P (2 2,0) is y=x-2, and x2- 16x+4=0 is obtained by substituting it into the parabolic equation.

∴x 1+x2= 16，

The distance from the midpoint of the chord AB to the parabolic directrix is x1+x2+P2 =11.

So the answer is: 1 1.