first check domain on both sides for sqrt(x^2-16) it is (-infinity to -4]U[4,infinity)

and for x+2 it is any real no

now sqrt(x^2-16)>=0

so x+2 takes positive values

so it can have domain as [0,infinity)

but we need to take in consideration the right hand side which contains square root term

if we split [0,infinity) into two parts i.e.

[0,4)U[4,infinity)

we see that [0,4) does not satisfy the domain for right hand side

so x belongs to [4,infinity)