To solve the expression, we will first simplify the calculation:

4/9 * 15/28

First, we can simplify 15/28 by finding the greatest common divisor between 15 and 28. The greatest common divisor is 1, so we cannot simplify this fraction further.

Now we multiply the fractions:
4 15 = 60
9 28 = 252

Therefore, the result of 4/9 * 15/28 is 60/252.

Now the expression is 60/252 : 5/18 * 10/27

To divide fractions, we multiply by the reciprocal of the second fraction:

60/252 18/5 10/27
= (60 18 10)/(252 5 27)
= 10800 / 34020
= 180 / 567
= 20 / 63

Therefore, the simplified result of 4/9 15/28 : 5/18 10/27 is 20/63.