When two 2-digit numbers are multiplied together, such as 31X32, it is easy to know the first and last numbers of the answer:
Multiply the tens digits together for the first numbers of the answer, and the ones digits together for the last number of the answer. In this case, 3X3=9 and 1X2=2, so we have 9 _ 2.
To get the middle number:
Multiply together the outer digits, and multiply together the inner digits, and these two figures added together give the middle digit of the answer. There may be a carry figure. In this case, we have (3X2)+(3X1)=9
The answer of our example is 991.
One may recognize this as the FOIL method of multiplying variables in algebra, with the letters representing multiplication steps: First, Outer, Inner, Last. When learning algebra, many wonder how it can be usefully applied, and this is one valuable way. FOIL makes multiplying many 2-digit numbers quite easy and quick, with practice.
Quickly, F: 2X6 gives 12 _ _.
Then, L: 4X2 gives 12 _ 8.
Lastly, (O+I): (2X2)+(6X4)=4+24 gives 28. This 8 is the middle digit of the answer, with the 2 carried to the first digits of the answer, making the first digits now 12+2=14.
The answer is 1488.
Practice, practice practice, using low digits at first to get the mind used to the process.