Answer: 20

An increase of $p\%$ multiplies the quantity by $1 + \frac{p}{100}$, and a decrease of $p\%$ multiplies it by $1 - \frac{p}{100}$. So $\left(1 + \frac{p}{100}\right)\left(1 - \frac{p}{100}\right) = 0.96$, which simplifies to $1 - \frac{p^2}{10{,}000} = 0.96$. Then $p^2 = 400$, and since $p > 0$, $p = 20$.

It's tempting to answer $4$ because the value drops by $4\%$, but a $4\%$ increase followed by a $4\%$ decrease leaves $99.84\%$ of the original value.