An easier way to do this mentally is:
Start with one of the numbers. I will use 78, in this example, but either is fine.
Now, multiply each digit of 78 each digit of 56. When doing this, be sure to take the place of the digit into account. For example, rather than doing 7 * 6, you need do to 70 * 6.
1. 8 * 6 = 48: Take the number in the one's place of 78, and multiply it by the 6 of 56.
2. 8 * 50 = 400: Now, take the number in the one's place of 78, and multiply it by the next digit in 56, which would be 5. However, the 5 in 56 actually represents 50, so you need to take that into account.
3. 70 * 6 = 420: Now that you have multiplied the digit in the one's place by each digit of the other number, move onto the next digit. Once again, to forget to take into account what that digit actually represents -- it represents seven tens, or seventy! Repeat this until there are no more digits to multiply.
4. 70 * 50 = 3500
5. 3500 + 420 + 400 + 48 = 4368. : Now, add all those results together to get your answer!
78 * 56 = 4368