Homomorphisms and Isomorphisms · Easy problem

Define $\varphi: \mathbb Z_2 \times \mathbb Z_3 \to \mathbb Z_6$ by sending $(a,b)$ to the unique $x \in \{0,\dots,5\}$ with $x \equiv a \pmod 2$ and $x \equiv b \pmod 3$ (this is the isomorphism from the Chinese Remainder Theorem). Find $\varphi(1,2)$.