The units digit repeats in a pattern of 4 numbers -- the same pattern as raising 2 to a power (because 2 is the last digit of the given number).
Take the exponent from your problem, 134. Do integer division by 4 (the kind you first learned in 2nd or 3rd grade where you get a quotient and a remainder). If the remainder is 1, the units digit is 2. If the remainder is 2, the units digit is 4, 3 means 8, and 0 means 6.
John
My calculator said it, I believe it, that settles it