Step 1: Calculate the total number of batteries needed for the basic calculators. 20 basic calculators * 3 batteries per calculator = 60 batteries needed for the basic calculators.

Step 2: Calculate the total number of batteries needed for the advanced calculators. 12 advanced calculators * 4 batteries per calculator = 48 batteries needed for the advanced calculators.

Step 3: Calculate the total number of batteries needed for all the calculators. 60 batteries for the basic calculators + 48 batteries for the advanced calculators = 108 batteries needed in total.

Step 4: Calculate the number of batteries in each package. 24 batteries per package.

Step 5: Calculate the number of packages needed. 108 batteries needed / 24 batteries per package = 4.5 packages needed.

Step 6: Determine if the teacher’s estimate of 6 packages is correct. Since the teacher estimated that 6 packages of batteries will be needed, and we calculated that only 4.5 packages are needed, the teacher’s estimate is incorrect.

Step 7: Calculate the number of batteries left over. 4.5 packages * 24 batteries per package = 108 batteries. 108 batteries - 108 batteries needed = 0 batteries left over.

Step 8: Determine if the teacher’s estimate of 12 batteries left over is correct. Since we calculated that there are 0 batteries left over, the teacher’s estimate of 12 batteries left over is incorrect.

In conclusion, the teacher’s estimate of needing 6 packages of batteries and having 12 batteries left over is incorrect. The correct number of packages needed is 4.5, which means that 5 packages should be purchased. Additionally, there will be no batteries left over after filling all the calculators.