To simplify this expression, we first need to find a common denominator for each of the fractions:

19/24 can be written as 15/20
4/15 remains as 4/15

7/10 can be written as 21/30
6/15 can be written as 12/30

Now we can plug in the new fractions into the expression:

(15/20 - 4/15) - (21/30 - 12/30)

Now, we can simplify by finding the common denominator for each set of fractions in the parentheses:

((225/300 - 80/300) - (126/300 - 72/300))

Now we subtract the fractions inside the parentheses:

(145/300) - (54/300)

Now subtract the two fractions:

145/300 - 54/300 = 91/300

So, the final answer is 91/300.