Division in Z4×Z2:
In order to understand what g/h is isomorphic to, we first need to understand how division works in the group Z4×Z2.

The group Z4×Z2 is the direct product of two groups: Z4 and Z2. Z4 is the group of integers modulo 4 under addition, and Z2 is the group of integers modulo 2 under addition.

The elements of Z4×Z2 are ordered pairs (a, b), where a is an element of Z4 and b is an element of Z2. Addition in Z4×Z2 is defined component-wise. That is, (a, b) + (c, d) = (a + c, b + d) mod 4.

Isomorphism:
An isomorphism is a bijective map between two groups that preserves the group structure. In other words, if two groups are isomorphic, they are essentially the same group with different labels on the elements.

In order to determine what g/h is isomorphic to, we need to consider the cosets of h in g. The cosets of h are the equivalence classes formed by adding h to each element of g.

Cosets of h in g:
To find the cosets of h in g, we add h to each element of g and reduce modulo 4.

g/h = {(a, b) + (2, 1) mod 4 | (a, b) ∈ Z4×Z2}

We can calculate the cosets of h in g as follows:

(0, 0) + (2, 1) = (2, 1) mod 4
(1, 0) + (2, 1) = (3, 1) mod 4
(2, 0) + (2, 1) = (0, 1) mod 4
(3, 0) + (2, 1) = (1, 1) mod 4

Therefore, the cosets of h in g are {(2, 1), (3, 1), (0, 1), (1, 1)}.

Isomorphism:
Now, we can determine what g/h is isomorphic to by comparing the structure of the cosets with other groups.

The cosets of h in g form a group under addition modulo 4. This group is isomorphic to Z4, the group of integers modulo 4 under addition.

Therefore, g/h is isomorphic to Z4.