Solution:

Given, there are 9 things which are to be divided into twice groups containing 2, 3, and 4 things respectively.

Let's assume the groups containing 2 things are A1 and A2, groups containing 3 things are B1 and B2, and groups containing 4 things are C1 and C2.

We need to find the number of ways in which we can divide 9 things into these groups.

Step 1: Selecting 2 things for group A1

The first group A1 can be selected in the following ways:

- Selecting any 2 things out of 9 things = 9C2 ways

Step 2: Selecting 2 things for group A2

The second group A2 can be selected in the following ways:

- Selecting any 2 things out of the remaining 7 things = 7C2 ways

Step 3: Selecting 3 things for group B1

The third group B1 can be selected in the following ways:

- Selecting any 3 things out of the remaining 5 things = 5C3 ways

Step 4: Selecting 3 things for group B2

The fourth group B2 can be selected in the following ways:

- Selecting any 3 things out of the remaining 2 things = 2C3 ways (which is 0)

Step 5: Selecting 4 things for group C1

The fifth group C1 can be selected in the following ways:

- Selecting any 4 things out of the remaining 2 things = 2C4 ways (which is 0)

Step 6: Selecting 4 things for group C2

The sixth group C2 can be selected in the following ways:

- Selecting the remaining 2 things as they all have been already selected in the above groups = 1 way

Hence, the total number of ways in which 9 things can be divided into twice groups containing 2, 3, and 4 things respectively is:

9C2 * 7C2 * 5C3 * 1 = 1260

Therefore, the correct option is (b) 1260.