`If A=(x:x= 4n,nin Z) and b={x:x = 6n,n in Z},`then `A capB` contains

Options

A. 16
B. 24
C. 28
D. 32

Explanation

To solve the problem, we need to find the intersection of the two sets \( A \) and \( B \).

### Step-by-Step Solution:

1. **Define the Sets**:
- Set \( A \) is defined as \( A = \{ x : x = 4n, n \in \mathbb{Z} \} \).
- Set \( B \) is defined as \( B = \{ x : x = 6n, n \in \mathbb{Z} \} \).

2. **Identify the Elements of Each Set**:
- The elements of set \( A \) are all multiples of 4: \( \ldots, -8, -4, 0, 4, 8, 12, 16, \ldots \).
- The elements of set \( B \) are all multiples of 6: \( \ldots, -12, -6, 0, 6, 12, 18, 24, \ldots \).

3. **Find the Common Elements (Intersection)**:
- The intersection \( A \cap B \) consists of elements that are common to both sets.
- To find common elements, we need to find the least common multiple (LCM) of 4 and 6.
- The LCM of 4 and 6 is 12.

4. **Express the Intersection**:
- Therefore, the intersection can be expressed as:
\[ A \cap B = \{ x : x = 12n, n \in \mathbb{Z} \} \]

5. **Conclusion**:
- The intersection \( A \cap B \) contains all multiples of 12, which can be written as:
\[ A \cap B = \{ \ldots, -24, -12, 0, 12, 24, \ldots \} \]

### Final Answer:
The intersection \( A \cap B \) contains \( \{ x : x = 12n, n \in \mathbb{Z} \} \).