= Solution
Integer row and column operations give
$$
\begin{pmatrix}-4&-6\\2&2\end{pmatrix}
\sim
\begin{pmatrix}2&2\\-4&-6\end{pmatrix}
\sim
\begin{pmatrix}2&2\\0&-2\end{pmatrix}
\sim
\begin{pmatrix}2&0\\0&2\end{pmatrix}.
$$
Thus the Smith normal form is
$$
\boxed{\operatorname{diag}(2,2)}.
$$
The two relation <vectors> are the columns of the displayed <matrix>, so its cokernel is the presented module. Consequently
$$
\boxed{M\cong\mathbb Z/2\mathbb Z\oplus\mathbb Z/2\mathbb Z}.
$$
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