how can this be???

for any real positive numbers, the inequality is:

AM ≥ GM ≥ HM

so if they’re giving you:

AM = 4 and GM = 8

that’s impossible in real numbers, because GM can never be greater than AM

this is just a flawed / inconsistent question. the relation

AM × HM = GM² is valid, so mathematically you can still plug values and get HM = 16, but the given values themselves don’t correspond to any real pair of numbers

if they give such values, just apply the formula they expect. But conceptually, you’re correct

I think it's just to test your algebraic knowledge, as the question in itself is conceptually invalid