How many different combinations can be made from a combination of 3 letters and 3 nuimbers?

Taking this bit by bit...

For each number there are 10 possibilities so three numbers has 10^3 which is 1000

for each letter there are 26 choices, so for three letters you have 26^3 which is 17576

together there are 17576 * 1000 options which makes 17576000 possible combinations of letters and numbers and I suspect that is what you want.

However if the order of the combination is important you must take into account the position of each letter/number and remove duplicate combinations. Good luck with that