To find the greatest number which divides 126, 150, and 210 leaving a remainder of 6 in each case, we can use the concept of the highest common factor (HCF) or greatest common divisor (GCD).

The HCF or GCD of a set of numbers is the largest number that divides all the given numbers without leaving any remainder.

We are given three numbers - 126, 150, and 210 - and we are looking for a number that divides all three numbers leaving a remainder of 6.

Let's find the factors of each number and see if we can find a common factor that satisfies the given conditions.

Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Factors of 210: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

From the factors listed above, we need to find a number that divides all three numbers leaving a remainder of 6.

The common factors that satisfy this condition are:
- 2 (divides all three numbers leaving a remainder of 0, not 6)
- 3 (divides all three numbers leaving a remainder of 0, not 6)
- 6 (divides all three numbers leaving a remainder of 0, not 6)
- 14 (divides all three numbers leaving a remainder of 6)

Out of these common factors, the greatest number is 14. Therefore, the greatest number which divides 126, 150, and 210 leaving a remainder of 6 in each case is 14.

Hence, the correct answer is option 'A' - 14.

A is the answer because 12 ➗ by 126 is the ans 6