Find an isomorphic direct product of cyclic groups, where $V$ is an abelian group generated by $x,y,z$ and subject to relations: $$3x + 2y + 8z = 0,\qquad 2x + 4z = 0.$$
The answer is $C_{4} \oplus \mathbb{Z}$
But I don't know how to get the answers.