The expression x⁴ – 8x² + m will be a perfect square when the value of m is:

16

When x⁴ – 8x² + m is a perfect square then m must be a square also.

So, if we go through the options only 2nd and fourth options are the perfect square that are 16 and 4.

So if we take 16 , x⁴ – 8x² + 16  is the square of (x² + 4)²

The answer is m = 16.