6.(A)
This is not time-invariant.
1. input($ /delta[n-k] $) -> system -> time delay (1) -> output : $ (k+1)^2\delta[n-(k+2)] $
2. input($ /delta[n-k] $) -> time delay (1) -> system -> output : $ (k+2)^2\delta[n-(k+2)] $
The output signals are different each other. So this is not time-invariant.
6.(B)
Because of assuming this system is linear, the input should be x[n].
