The amount of water used to make pancakes varies directly with the amount of pancake mix. If nine cups of mix requires three cups of water, then six cups of mix requires $\checkmark$ cups of water.

Step 1 ：This is a problem of direct variation. In direct variation, the ratio between two quantities remains constant. In this case, the ratio between the amount of pancake mix and the amount of water is constant. We can set up a proportion to solve for the unknown amount of water.

Step 2 ：Let's denote the amount of pancake mix as 'mix' and the amount of water as 'water'. From the problem, we know that when mix1 = 9, water1 = 3. We are asked to find the amount of water (water2) when mix2 = 6.

Step 3 ：We can set up the proportion as follows: \(\frac{mix1}{water1} = \frac{mix2}{water2}\)

Step 4 ：Substituting the given values into the proportion, we get: \(\frac{9}{3} = \frac{6}{water2}\)

Step 5 ：Solving for water2, we find that water2 = 2.0

Step 6 ：Final Answer: The amount of water required for six cups of mix is \(\boxed{2}\) cups.