Simultaneous Multiple Choice Linear Congruence Question 2

For which of the following 4-tuples of integers do we have a solution to the system of simultaneous linear congruences:

The first thing to notice here is that we have three different mods however all three are not different as required for Chinese remainder theorem. So we do for first two mods 2 and 3 and check for the third one mod 6. We may also have to check the relation between mod 4 and mod 2