You poured some $12 \%$ alcohol solution and some $6 \%$ alcohol solution into a mixing container. Now you have 480 grams of $8 \%$ alcohol solution. How many grams of $12 \%$ solution and how many grams of $6 \%$ solution did you pour into the mixing container? Write and solve a system equation to answer the following questions. You mixed $\square$ grams of $12 \%$ solution with $\square$ grams of $6 \%$ solution.

Step 1 ：Let's denote the amount of $12 \%$ solution as \(x\) and the amount of $6 \%$ solution as \(y\).

Step 2 ：From the problem, we know that the total amount of solution is 480 grams, so we have the equation \(x + y = 480\).

Step 3 ：We also know that the final solution is $8 \%$ alcohol, so the total amount of alcohol from the $12 \%$ solution and the $6 \%$ solution should be $8 \%$ of the total solution. This gives us the equation \(0.12x + 0.06y = 0.08 \times 480\).

Step 4 ：We can solve the first equation for \(x\), which gives us \(x = 480 - y\).

Step 5 ：Substitute \(x = 480 - y\) into the second equation, we get \(0.12(480 - y) + 0.06y = 38.4\).

Step 6 ：Solving this equation for \(y\), we get \(y = 320\).

Step 7 ：Substitute \(y = 320\) back into the first equation, we get \(x = 480 - 320 = 160\).

Step 8 ：So, the final answer is: You mixed \(\boxed{160}\) grams of $12 \%$ solution with \(\boxed{320}\) grams of $6 \%$ solution.