= Solution
Change the generators to $a=m_1$, $b=m_3-m_2$ and $c=m_2$. This is an invertible <integer> change of generators, since $m_1=a$, $m_2=c$, $m_3=b+c$. The relations become $2b=0$ and $4c=0$, with no relation involving $a$. Consequently
$$
\boxed{M\cong\mathbb Z\oplus\mathbb Z/2\mathbb Z\oplus\mathbb Z/4\mathbb Z.}
$$
This is already the invariant-factor order required by the <structure theorem for finitely generated modules over a principal ideal domain>, because $2\mid4$. The inverse change of generators shows that there are no hidden extra relations.
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