The rule for 3-digit multiplication is illustrated if we write the multiplication as:
ABC
×DEF
We work from right to left, that is, from the ones to the ten thousands.
(Ones column) Step 1: Multiply C and F and if there's a carry write it under the tens column.
(Tens column) Step 2: Cross-multiply and add: B×F+C×E and add the carry, if any, from step 1. If there's another carry write it under the hundreds column. Note the pattern of multiplication here: we move left to right on the first number and right to left on the second number.
(Hundreds column) Step 3: Cross-multiply and add: A×F+B×E+C×D and add the carry, if any, from step 2. Write any carry under the thousands column.
(Thousands column) Step 4: Cross-multiply and add: A×E+B×D and add the the carry, if any, from step 3. Write any carry under the ten thousands column.
(Ten thousands column) Step 5: Multiply A and D and add any carry from step 4.
Example: 123×456.
Step 1: 3×6=18. 8 ones and carry=1 for the tens column.
Step 2: 2×6+3×5=27 plus carry from step 1=28. 8 tens and carry=2 for the hundreds column.
Step 3: 1×6+2×5+3×4=28+2 (carry)=30. 0 hundreds and carry=3 for the thousands column.
Step 4: 1×5+2×4=13+3 (carry)=16. 6 thousands and carry=1 for the ten thousands column.
Step 5: 1×4=4+1=5.
RESULT= 56088