03NS30

The rule for divisibility by 8 is that, if the last three digits are divisible by 8, then the whole number is divisible by 8

The total number of outcomes is  6^8

Notice that  the smallest that the last three digits can be  =  111

And the largest that they can be  = 666

The number of integers between these two numbers that are divisible by 8  =

floor [ (666 - 111) / 8 ]  = 69

So....the number of outcomes that are divisible by 8  =  (6)^5 * 69

So the probability  =   (6)^5 * 69  /  (6)^8   =   69 / 6^3   =   69 / 216   =  23 / 72

Wait, won't some of them contain digits larger than 6?