so, whenever you take an "even root" of a "negative value", you'd end up with an imaginary root or value, which is another way to say, such root doesn't really exist or no solution.
now, we can look at it this way, the same equation is really just a parabola like (x+2)² + 16 = 0, notice, the parabola is in vertex form, its vertex is at (-2 , 16), on the II Quadrant 16 units up above the x-axis. A solution or what's called a solution or root or zero is really nothing but just an x-intercept, well, the parabola's vertex is way up and is opening upwards, so it never touches the x-axis, no zeros, no solution.
Check the picture below.