The grocery store we use does not mark prices on its goods. My wife went to this store, bought three packages of bacon and four cartons of eggs, and paid a total of $\$ 14.43$. Not knowing that she went to the store, 1 also went to the same store, purchased four packages of bacon and three cartons of eggs, and paid a total of $\$ 16.93$. Now we want to return three packages of bacon and three cartons of eggs. How much will be refunded? How much will we be refunded?

Step 1 ：Let's denote the price of a package of bacon as \(B\) and the price of a carton of eggs as \(E\).

Step 2 ：From the information given, we can form two equations. The first equation is from the wife's purchase: \(3B + 4E = 14.43\). The second equation is from the husband's purchase: \(4B + 3E = 16.93\).

Step 3 ：We can solve this system of equations to find the values of \(B\) and \(E\).

Step 4 ：The solution to the system of equations is \(B = 3.49\) and \(E = 0.99\).

Step 5 ：Now, we want to find out how much will be refunded for returning three packages of bacon and three cartons of eggs. This can be calculated as \(3B + 3E\).

Step 6 ：Substituting the values of \(B\) and \(E\) into the equation, we get the refund amount as \(13.44\).

Step 7 ：So, the refund will be \(\boxed{13.44}\) dollars.