x=1(mod 4) implies x=1(mod 2) (you can drop this one).
x=1(mod 6) implies x=1(mod 2 and 3) (you can drop this one).
Thus, you get,
(I deleted you other question on Chinese Remainder Theorem, because it seems to me you just want the answer. You want me to help you, you show the work you done so far. Because otherwise that makes me angry. You insult my intellegence! )