First "beneath xy+ yz" makes no sense. In order to have a surface that must be equal to something. What is it equal to?
The equation of the sphere with center (1, 1, 1) with radius 2 is .
In spherical coordinates, , , . Put those into the equation of the sphere and plane.
However, you might find it simpler to shift the entire problem so that the center of the sphere is at the origin. That is, let u= x- 1, v= y- 1, w= z- 1 so that in the uvw- coordinate system the sphere is given by and the surface xy+ yz= f(x,y,z) becomes (here f is the missing part of the equation of the surface).
Now replace u, v, and w with , , and .
(Depending on exactly how the lower surface is defined, you might find it simpler to use cylindrical coordinates.)