A number is first increased by $20\%$ and then decreased by $20\%$. What is the net percentage change?

Let the original number be $100$.
1. First, the number is increased by $20\%$:

$$\text{New number}=100+\left(\frac{20}{100}\times 100\right)=120$$

2. Then, the new number is decreased by $20\%$:

$$\text{Final number}=120-\left(\frac{20}{100}\times 120\right)=120-24=96$$

3. Net percentage change calculation:

$$\text{Net Change}=\text{Original Number}-\text{Final Number}=100-96=4$$

Since the final number is less than the original number, it is a $4\%$ decrease.

Alternative Method (Formula):
Net change percentage when a value is successively changed by $+x\%$ and $-y\%$:

$$\text{Net Change}=x-y-\frac{x\times y}{100}$$

$$\text{Net Change}=20-20-\frac{20\times 20}{100}=-4\%$$

The negative sign indicates a decrease of $4\%$.