1. **State the problem:** We have a bag with 4 red balls and 2 white balls. We want to add some white balls so that the probability of picking a red ball equals the probability of picking a white ball. 2. **Define variables and formula:** Let $x$ be the number of white balls to add. The total number of balls after adding is $4 + 2 + x = 6 + x$. The probability of picking a red ball is $\frac{4}{6+x}$. The probability of picking a white ball is $\frac{2+x}{6+x}$. 3. **Set the probabilities equal:** $$\frac{4}{6+x} = \frac{2+x}{6+x}$$ Since denominators are the same and nonzero, set numerators equal: $$4 = 2 + x$$ 4. **Solve for $x$:** $$x = 4 - 2 = 2$$ 5. **Interpretation:** Adding 2 white balls makes the number of white balls equal to the number of red balls (4 each), so the chance of picking either color is equal. **Final answer:** $2$ white balls should be added.