Preserve the absolute deviation when relating two normal tails

Independent X,Y have distributions $N(2\mu,\sigma^2)$ and $N(3\mu,3\sigma^2)$ respectively, with σ>0. Let $Z\sim N(0,1)$.

(i) Given $P(X<2\mu+2\sigma^2)=k$, show that $P(Z<2\sigma)=k$.

(ii) Write down the mean and variance of Y−X. Hence find $P(|Y-X-\mu|>4\sigma^2)$ in terms of k.