To find the value of the expression, we first need to find a common denominator for all the fractions involved.

1/4 can be written as 3/12
0.6 can be written as 6/10 = 3/5
1/15 can be written as 2/30
0.125 can be written as 1/8

Therefore, the expression becomes:
3/12 + 3/5 + 2/30 + 1/8
= 15/60 + 36/60 + 4/60 + 7/60
= 62/60
= 31/30

Now, to divide by 1/24, you invert and multiply:
31/30 ÷ 1/24
= 31/30 24/1
= 31 24 / 30
= 744 / 30
= 124/5

Thus, the final result of the expression divided by 1/24 is 124/5.