The given sets are:
$$A=\left\{x:x\in N \right\}=\left\{1,2,3,4..... \right\}$$
$$B=\left\{x:x=2n, n\in N \right\}=\left\{2,4,6,8,10.... \right\}$$
$$C=\left\{x:x=2n-1, n\in N \right\}=\left\{1,3,5,7,9....... \right\}$$
$$D=\left\{x:x\ is\ a\ prime\ number \right\}=\left\{2,3,5,7,11,13.... \right\}$$
$$\therefore \ A\cap B=\left\{1,2,3,4.... \right\} \cap \left\{2,4,6,8.... \right\}$$
$$=\left\{2,4,6,8.... \right\}$$
$$=B$$
Hence $$\boxed {A\cap B=B}$$