Step 1) suppose we have a1a2 * b1b2, multiply b2 with a2 first that is b2 * a2, if any carry is generated transfer it to previous digit, and now multiply b2 with a1 that is b2 * a1 and add the carry to result of b2 * a1 and write the result.

Step 2) Now multiply b1 with a2 that gives b1 * a2 if carry is generated transfer it to previous digit, now multiply b1 with a1 which gives us b1 * a1 and add the carry to result of b1 * a1 and write the result and shift the result to left by one place.

Step 3) now add the results of step 1 and step 2.

Step 4) Final Result

Let us take some examples to understand 2 digit multiplication strategies-

Example 1) 25 * 44, steps for this multiplication are shown below-

Carry= 2

25

* 44

----------

100

100*

----------

Result=1100

Step 1) Multiply 4 with 5 which gives us 20, so 2 will go as carry, so 0 is result.

Step 2) Multiply 4 with 2 which gives 8 and add 2 so result is 100.

Step 3) Follow same procedure for previous digit.

Step 4) Now add results we 1100, which is our final result.

So two digit multiplication is similar to single digit multiplication, we multiply digits in each step and finally add results of those multiplications which is our final answer.