To find the value of the expression when a = -3.14, we substitute a = -3.14 into the expression and simplify.

First, substitute a = -3.14 into each part of the expression:

(a + 4)(a^2) - 8a - 16
(-3.14 + 4)(-3.14)^2 - 8(-3.14) - 16
(0.86)(9.8596) + 25.12 - 16
8.4686 + 25.12 - 16
17.5886

a|a|
-3.14|-3.14|
3.14*3.14
9.8596

Now substitute these values back into the expression:

|17.5886| + 9.8596
17.5886 + 9.8596
27.4482

Therefore, when a = -3.14, the value of the expression is 27.4482.