If  $2|x^2-4|=x^2-4x+a$ has exactly three distinct solutions then sum of all possible value of ‘3a’ is _______

Case-I
When for ‘3’ solution
$y=x^2-4x+a$  touches
$y=8-2x^2$  in  $[-2,2]$
 $\Rightarrow x^2-4x+a=8-2x^2$
$\Rightarrow 3x^2-4x+a-8=0$  has exactly one root
16 – 12(a – 8) = 0
 $\Rightarrow 4-3a+24=0\Rightarrow 28=3a$
 $\Rightarrow a=\frac{28}{3}$
 
(Note: L.R. of $y=x^2-4x+a>L.R.ofy=2x^2-8$ )
Case-II
 
When  $y=x^2-4x+a$  passes through (2, 0)
a = 4