Pair up the counters. If every one has a partner, the number is even. If one is left over, it's odd.
Can all 20 counters find a partner?
Even: every counter has a partner.
Odd: one is left over.
The last digit tells you: 0, 2, 4, 6 and 8 are even.
A number that can be shared into pairs with none left over, like 8: four pairs. Even numbers end in 0, 2, 4, 6 or 8. Every even number is in the 2 times table.
A number that leaves one left over when you put it into pairs, like 7: three pairs and one more. Odd numbers end in 1, 3, 5, 7 or 9.
Just look at the last digit. 3,458 ends in 8, so it is even. 901 ends in 1, so it is odd. The other digits are tens, hundreds and thousands, which can always be put into pairs, so they never change the answer.
Children start pairing objects and spotting odd and even numbers at about 5 to 7, and use the last digit to sort bigger numbers at about 7 to 8.