This techniqu is called the cross-multiplication technique...

Lets start with 123 * 456.

^Step 1--- arrange the numbers in order (one on top of the other) your pick.

123
456
----------

start by first multiplying 6*3=18. write down the 8 and carry the 1 mentally.

123
456
---------- CARRY 1
----8

^Step 2---- attempt to form an invisible X
It may not sound simple at first but I'll explain.

Start by observing the 6 & 2, then the 5 & 3. Make a line between those numbers and you will get an X.

Now multiple 6*2=12 PLUS(+) 5*3=15
so 12 + 15 = 27
27 + 1 (the carry)= 28
Now write down the 8 and carry the 2 mentally.

123
456
---------- CARRY 2
---88


^Step 3--- now examine the numbers 6 & 1, 4 & 3, then in the middle 2 & 5.

Multiply them and add em' all up:
6*1=6 + 4*3=12 + 5*2=10
so 6 + 12 +10 = 28 PLUS carry 2 = 30.

Write down the 0 and carry the 3.

123
456
---------- CARRY 3
--088

^Step 4--- Now we will attempt the invisible X for the last time. This time take notice of the numbers 5 & 1, 4 & 2
multiply them and add em' all up:
5*1=5 + 4*2=8
so 5 + 8 = 13 PLUS carry 3 = 16.
Write down the 6 and carry the 1.

123
456
---------- CARRY 1
--6088

^Step 5 (final step)--- In the beginning we started by multiplying 6 & 3. Now we will multiply 4 & 1.
so 4*1=4 + carry 1 = 5

Write it down and the behold the FINAL ANSWER!

123
456
----------
56088