To solve this problem, we can use the Chinese Remainder Theorem. According to the theorem, if a number leaves remainders 2 when divided by 3, 5, and 7, then it can be represented in the form:

x ≡ 2 (mod 3)
x ≡ 2 (mod 5)
x ≡ 2 (mod 7)

We can solve these congruences simultaneously to find the value of x.

Solution:
1. Solve the first two congruences:
x ≡ 2 (mod 3)
x ≡ 2 (mod 5)

To solve these congruences, we can find the least common multiple (LCM) of 3 and 5, which is 15.

Multiples of 15: 15, 30, 45, 60, 75, ...

Among these multiples, the first one that satisfies both congruences is x = 2 (mod 15).

2. Solve the third congruence:
x ≡ 2 (mod 7)

To find a solution, we can start from x = 2 and add multiples of 7 until we find a solution.

Multiples of 7: 7, 14, 21, 28, 35, ...

Among these multiples, the first one that satisfies the congruence is x = 2 (mod 7).

3. Combine the solutions:
Now, we have two congruences that are both satisfied:
x ≡ 2 (mod 15)
x ≡ 2 (mod 7)

We can find the LCM of 15 and 7, which is 105.

Multiples of 105: 105, 210, 315, 420, ...

Among these multiples, the first one that satisfies both congruences is x = 2 (mod 105).

Therefore, the number x that satisfies all three congruences is x = 2 (mod 105).

To find the remainder when x is divided by 9, we can use the property of modular arithmetic that states:

If a ≡ b (mod m), then a ≡ b + km (mod m) for any integer k.

In this case, we can write:
x ≡ 2 + 103(105) (mod 105)

Since 103(105) is divisible by 9, the remainder of x when divided by 9 is the same as the remainder of 2 when divided by 9, which is 2.

Therefore, the correct answer is option 'B': 8.