How many two digit numbers can be made from the digits of 345?

The digits of 345 are 3, 4, and 5. To form a two-digit number, we can choose any of the three digits for the tens place and any of the three digits for the units place. However, since a two-digit number cannot start with 0 and all three digits are non-zero, we can use all three digits. Thus, we have 3 choices for the first digit and 3 choices for the second digit, resulting in (3 \times 3 = 9) two-digit numbers.