There are 4 types of 3 digit numbers that can be made with them.
They are:

ABC, AAB, ABA, ABB

An example of type ABC would be 241.
An example of type AAB would be 221.
An example of type ABA would be 343.
An example of type ABB would be 322.

Case 1:  ABC
Choose the digit for A any of 4 ways {1,2,3,4}.
Choose the digit for B any of the remaining 3 ways.
Choose the digit for C any of the remaining 2 ways.

Total for case 1: 4*3*2 = 24 ways.

Case 2:  AAB
Choose the digit for A any of 2 ways {2,3}
Choose the digit for B any of the remaining 3 ways.

Total for case 2: 2*3 = 6 ways. 

Case 3: ABA
Same as Case 2:

Total for Case 3: 6 ways.


Case 4:  ABB
Same as Case 2:

Total for Case 4: 6 ways.

Grand total: 24+6+6+6 = 42

Edwin