Find the least common denominator (LCD). See what number is a multiple of both denominators 8 and 6. Since both 8 and 6 go into 24, we use that.
Now multiply each numerator by the number that its denominator is multiplied by to get 24.
So for 1/8: 8×3 = 24, so 1×3 = 3
That fraction becomes 3/24
For 1/6: 6×4 = 24, so 1×4 = 4
That fraction becomes 4/24
Now subtract the two fractions:
3/24 - 4/24 --> only add the numerator and keep the common denominator, so (3 - 4)/24 = -1/24
Last step is to simply, but since no number goes into both 1 and 24 except for 1, -1/24 is already in its simplest form.