To simplify the expression 4/15(1 1/2n -4,5)-1 1/2(8/27n+5,4), we will first convert all mixed numbers to improper fractions and then distribute the coefficients.

1 1/2 can be converted to 3/2, and 1 1/2 = 3/2.

So the expression becomes:

4/15 (3/2n - 9/2) - 3/2 (8/27n + 27/5)

Next, distribute the coefficients:

(4/15 3/2n) - (4/15 9/2) - (3/2 8/27n) - (3/2 27/5)

= 2/5n - 6/5 - 8/90n - 81/10

Now, simplify each term:

= 2/5n - 6/5 - 4/45n - 81/10
= (2/5 - 4/45)n - 6/5 - 81/10
= (18/45 - 4/45)n - 6/5 - 81/10
= 14/45n - 6/5 - 81/10

Therefore, the simplified expression is:

14/45n - 6/5 - 81/10