how many natural numbers not exceeding 4321can be formed with the digits 1,2,3,4 if the digits can repeat?

Anyway, there are 4 one digit numbers (obvious)
16 two digit numbers (there are 4 options for each digit, and two digit numbers are automatically <= 4321)
64 three digit numbers (again, 4 options for each digit)

Now for the four digit numbers:
There are 64 numbers where the first digit is a 3 (4 options for each of the remaining digits, and since the first digit is a 3, the number is < 4321)

Similarly there are 64 numbers where the first digit is a 2, and another 64 where the first digit is a 1.
This is 192 four digit numbers so long.

Now lets look at what happens if the first digit is a 4.
There are 16 numbers where the second digit is a 2 (the last two digits can be anything in this case) and another 16 where the second digit is a 1.
If the second digit is a 3:
...If the third digit is a 1, there are 4 numbers, because there are no restrictions on the last digit.
...If the third digit is a 2, there is only one possible number, n.l. 4321.

So, there are 16 numbers if the second digit is a 2, 16 numbers if the second digit is a 1, and 4 + 1 = 5 numbers if the second digit is a 3, giving
16 + 16 + 5 = 37 four digit numbers where the first digit is a 4.

In total, we have
4 one digit numbers
16 two digit numbers
64 three digit numbers
192 four digit numbers where the first digit is not a 4
37 four digit numbers where the first digit is a 4

This is 313 numbers in total.