Find the greatest number which leaves 4 when divided by 102 and leaves 3 when divided by 150.

Can anyone of you can please explain me the solution for this problem in detail.

Possible numbers that meet the first requirement are:

106, 208, 310, 412, 516 etc.
Possible numbers that meet the second requirement are: 153, 303, 453, 603 etc.
All the numbers on the first list are even and all on the second list are odd.
There is no number that satisfies both conditions and therefore no solution.