Answer
$\varnothing$, no solution
Work Step by Step
We have given,
$A=\{x|x$ is an even integer $\}$ $=\{...,-4,-2,0,2,4,6,8,10,...\}$ and
$B=\{x|x$ is an odd integer $\}=\{...,-3,-1,1,3,5,7,9,...\}$ Hence $A\cap B =$ the elements which are common in both A and B $=\varnothing$, since no integers are even and odd at the same time.