Multiplying three-digit numbers by three-digit numbers can seem daunting at first, but there are techniques you can use to make the process faster and more efficient. One popular method is the "long multiplication" technique. Here's how it works:

Let's say you want to multiply a three-digit number (ABC) by another three-digit number (DEF).

**Step 1**: Multiply the units digit (C) of the first number (ABC) by the second number (DEF), then write down the result.

**Step 2**: Multiply the tens digit (B) of the first number (ABC) by the second number (DEF), and write down the result shifted one position to the left (adding a zero as a placeholder at the rightmost end).

**Step 3**: Multiply the hundreds digit (A) of the first number (ABC) by the second number (DEF), and write down the result shifted two positions to the left (adding two zeros as placeholders at the rightmost end).

**Step 4**: Add up the three results you obtained from steps 1, 2, and 3. This will give you the final product of the multiplication.

Let's go through an example:

**Example: 345 * 678**

**Step 1**: 345 * 8 = 2760

**Step 2**: 345 * 7 = 2415 (shifted one position to the left: 24150)

**Step 3**: 345 * 6 = 2070 (shifted two positions to the left: 207000)

**Step 4**: Add 2760 + 24150 + 207000 = 234910

So,__ 345 * 678 = 234910__.

By practicing this method and becoming familiar with the steps, you can perform three-digit by three-digit multiplication more efficiently over time. Remember, practice and familiarity with the method will lead to increased speed and accuracy.