To simplify this expression, we first need to find a common denominator for the fractions involved.

-3/4x(20/9 - 8/15) - 9/10 ÷ 3/5

First, let's find a common denominator for 9 and 15, which is 45.

-3/4x(20/9 - 8/15) = -3/4x(100/45 - 24/45) = -3/4x(76/45)

Next, let's simplify the division of fractions:

-9/10 ÷ 3/5 = -9/10 x 5/3 = -45/30 = -3/2

Now, we can substitute these simplified fractions back into the original expression:

-3/4x(76/45) - 3/2

To simplify further, we can multiply the fractions:

-3/4 x 76/45 = -228/180 = -57/45

Now, the expression becomes:

-57/45 - 3/2

To combine these fractions, we need to find a common denominator, which is 2:

-57/45 - 3/2 = -57/45 - 67/45 = -124/45

Therefore, the simplified expression is -124/45.