To simplify this expression, we need to follow the order of operations (PEMDAS/BODMAS).

First, let's simplify the numerator:
5.4^15.9^2 = (5.4^15.9)^2
Using a calculator, we find that 5.4^15.9 ≈ 1.285 x 10^12
So, (5.4^15.9)^2 ≈ (1.285 x 10^12)^2 = 1.651 x 10^24

Next, let's simplify the denominator:
(-3)^20.8^9 = (-3)^(20.8^9)
Using a calculator, we find that 20.8^9 ≈ 1.097 x 10^15
So, (-3)^(20.8^9) ≈ (-3)^(1.097 x 10^15) = undefined (since raising a negative number to a large exponent is not defined)

Now, let's simplify the second term in the numerator:
4.(-3)^20.8^9 = 4.(-3)^(20.8^9)
Using a calculator, we find that 20.8^9 ≈ 1.097 x 10^15
So, 4.(-3)^(20.8^9) = 4.(-3)^(1.097 x 10^15) = undefined

Now, let's simplify the first term in the denominator:
5.(-2)^10.6^12 = 5.(-2)^(10.6^12)
Using a calculator, we find that 10.6^12 ≈ 2.374 x 10^12
So, 5.(-2)^(10.6^12) = 5.(-2)^(2.374 x 10^12) = undefined

Finally, let's simplify the second term in the denominator:
17.(-2)^29.27^6 = 17.(-2)^(29.27^6)
Using a calculator, we find that 29.27^6 ≈ 1.156 x 10^12
So, 17.(-2)^(29.27^6) = 17.(-2)^(1.156 x 10^12) = undefined

Now, let's evaluate the expression:
(1.651 x 10^24 - undefined) / (undefined + undefined) = undefined / undefined = undefined

Therefore, the value of the expression is undefined.