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Since 6 is an even number, its multiples are all even numbers as well. This means that each of its multiples ends in an even number (0, 2, 4, 6, 8). Since 3 is an odd number, any integer ending in a 3 is odd, thus proving that the number is not a multiple of 6.

cause 6 is even and any number multiply by an even number is even

Obviously any number ending with a 3 is odd

6 = 3 x 2

6 x Z = 3 x 2 x Z so the number is even and therefore cannot ends in 1, 3, 5, 7 or 9

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Q: Why a number cannot ends in 3 cannot be in the 6 times table?
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