To solve this expression, we first need to distribute the coefficients:

5/6(4.2x) - 5/6(1 1/5y) - 5.4(2/9x) + 5.4(1.5y)

Now, we can simplify by multiplying:

(20/3)x - (25/6)y - (8/15)x + 27/5y

Now, combine like terms:

(20/3 - 8/15)x - (25/6 + 27/5)y

Now, we can simplify further:

((100/15 - 24/15)x) - ((125/30 + 162/30)y)
(76/15)x - (287/30)y

So, the simplified expression is:

(76/15)x - (287/30)y