  We use the theta lifts between Mp(2) and PD to study the distinction problems
for the pair (Mp(2,E), SL(2,F )), where E is a quadratic field extension over a
nonarchimedean local field F of characteristic zero and D is a quaternion
algebra. With a similar strategy, we give a conjectural formula for the
multiplicity of distinction problem related to the pair (Mp(2n,E),Sp(2n,F)).
