If you multiply me by 2, I become a number greater than 20 and less than 40. If you multiple me by 6, I end in 8. If you multiply me by 4, I end in 2. Who am I?

Ok, for clarity, let's try and break down these clues into formulas using the variable x:

If you multiply me by 2, I become a number greater than 20 and less than 40

40 > 2x >20

This can be simplified by dividing all three figures by 2, so we get:

20 > x > 10

This narrows x down to a number between 20 and 10...

If you multiple me by 6, I end in 8.

6x = _8

Let's try some of the possibilities out:

6 * 10 = 60

6 * 11 = 66

6 * 12 = 72

6 * 13 = 78 (we've got a possible winner...)

6 * 18 = 108 (and another)

So we now know it's either 13 or 18, let's test the next rule:

4 * 13 = 52

4 * 18 = 72

Uhoh! Bit of a problem, they both pass that test. And that's the end of the line unfortunately. The answer can be either 13 or 18.