17 is odd.
1) If you add, subtract, or multiply 2 even numbers, the result will be even.
2) If you multiple an even and a odd number, the result is even.
So 3 is going to be key, being the only odd number.
You know that you cannot MULTIPLY 3 by any of the numbers, because that would produce an even number; and with only even numbers remaining, you could not get an odd number.
Therefore, 3 is going to have to be added to, or subtracted from, an even number, resulting in 17. So either:
14 + 3 = 17
20 - 3 = 17
Our task is now easier. Now we have only 3 numbers 2, 6, 8 remaining, and they are all even; and we need to get an even number from them.
With a few tries, we can see that:
2 x 6 + 8 = 20
So the final is:
2 x 6 + 8 - 3 = 17