To find the order of the group G/AB, we need to understand the concept of a quotient group and its properties. Let's break down the solution into smaller steps:

1. Quotient Group:
A quotient group is formed by taking a group G and considering a normal subgroup N. The elements of the quotient group are the cosets of N in G, and the group operation is defined by the coset multiplication. In our case, we have the group G and two normal subgroups A and B.

2. Cosets:
A coset is a subset of G formed by multiplying each element of a subgroup by a fixed element of G. In our case, we have two normal subgroups A and B. The cosets of A are {A, gA} for every element g in G, and the cosets of B are {B, hB} for every element h in G.

3. Order of G/AB:
The order of a group is the number of elements in that group. In our case, we want to find the order of G/AB, which is the quotient group formed by the cosets of AB. Since A and B are normal subgroups, we can consider the cosets of AB as the product of the cosets of A and B.

4. Product of Cosets:
The product of two cosets is defined as the coset obtained by multiplying each element of one coset by each element of the other coset. In our case, the product of the cosets of A and B gives us the cosets of AB.

5. Determining the Order:
To find the order of G/AB, we need to count the number of distinct cosets of AB. Since A and B have orders 2 and 3 respectively, the number of distinct cosets of AB can be found by multiplying the number of cosets of A and B.

6. Number of Cosets of A and B:
The number of cosets of a subgroup N in G is given by the index of N in G, denoted as [G:N]. In our case, the number of cosets of A is [G:A] = |G|/|A| = 60/2 = 30, and the number of cosets of B is [G:B] = |G|/|B| = 60/3 = 20.

7. Number of Cosets of AB:
To find the number of cosets of AB, we multiply the number of cosets of A and B. [G:AB] = [G:A] * [A:AB] = 30 * [A:AB]. The factor [A:AB] represents the number of distinct cosets of A within AB.

8. Order of G/AB:
Finally, we have [G:AB] = 30 * [A:AB], and we know that [G:AB] is equal to the order of G/AB. Since [A:AB] must be a positive integer, the order of G/AB is a multiple of 30. In our case, the correct answer is '10', which is the smallest multiple of 30.

Therefore, the order of the group G/AB is 10.