3. The number of all distinct integer solutions of the equation $2 x^{2}+5 x y+2 y^{2}=2012$ is ( ).
(A) 4
(B) 6
(C) 10
(D) 12
3. D.

The original equation can be transformed into
$$
(2 x+y)(x+2 y)=2^{2} \times 503 \text {. }
$$

Since the sum of $2 x+y$ and $x+2 y$ is divisible by 3, and $2^{2} \times 503$ can be factored into two integer factors (including negative factors), the sum of these two integer factors is also divisible by 3, so the number of solutions should be
$$
(2+1)(1+1) \times 2=12 \text {. }
$$