It is a little strange to give solutions for problems in a section which describes itself as having no solutions!
For all of the combinations of planes, we should find that the system of equations is inconsistent.
The geometric nature is either three parallel planes, two parallel planes intersected by a third, or three planes intersecting on parallel lines.
The parallel planes are C, E and F.
C E and F
A C and E
A C and F
A E and F
B C and E
B C and F
B E and F
C D and E
C D and F
D E and F
A B and C
A B and D
A B and E
A B and F
A C and D
A D and E
A D and F
B C and D
B D and E
B D and F