Does it means the remainder of that number divided by 6 is 0? I'm confused.
11 Answer
It does mean that the remainder is 0 when you divide that number by 6, or equivalently that the number is a multiple of 6, but that doesn't tell you what it really means.
When we say that "x = y mod 6", it doesn't mean that x = (y mod 6). "mod" is not an operator applied to y and 6. For example, it is correct to say that 4 + 3 = 1 mod 6. The "mod 6" means that we are working only with the remainders of numbers after division by 6, and not really working with the integers at all.
Note that this word "mod" is different from the modulus operator used in programming languages. Even though "4+3 = 1 mod 6" in English is true, "4+3 == 1%6" in C is false. In programming languages, % is an operator.