To find the HCF (Highest Common Factor) of two numbers, we need to determine the largest number that can evenly divide both of them.

To find the HCF of 18 and 48, we can use the following methods:

Method 1: Prime Factorization
- Determine the prime factors of both numbers.
- Prime factorization of 18: 2 × 3 × 3
- Prime factorization of 48: 2 × 2 × 2 × 2 × 3
- Identify the common factors: 2 and 3
- Multiply the common factors: 2 × 3 = 6
- Therefore, the HCF of 18 and 48 is 6.

Method 2: Division Method
- Divide the larger number (48) by the smaller number (18) and find the remainder.
- 48 ÷ 18 = 2 remainder 12
- Now, divide the smaller number (18) by the remainder (12) and find the new remainder.
- 18 ÷ 12 = 1 remainder 6
- Continue dividing the previous remainder (12) by the new remainder (6) until the remainder becomes zero.
- 12 ÷ 6 = 2 remainder 0
- The divisor at this point is the HCF of the two numbers.
- Therefore, the HCF of 18 and 48 is 6.

Both methods yield the same result, which is 6. Therefore, the correct answer is option B) 6.