Answer: (a) \(3024\); (b) \(24\); (c) \(240\); (d) \(1344\).

(a) The first digit can be chosen in \(9\) ways, the second in \(8\) ways, the third in \(7\) ways and the fourth in \(6\) ways.

Therefore the number of codes is

\(9\times8\times7\times6=3024.\)

(b) The prime numbers from \(1\) to \(9\) are \(2,3,5,7\). All four must be used, in any order, so the number of codes is

\(4!=24.\)

(c) The even numbers are \(2,4,6,8\), and the odd numbers are \(1,3,5,7,9\).

The first two positions are filled by two different even numbers:

\(4\times3=12.\)

The last two positions are filled by two different odd numbers:

\(5\times4=20.\)

So the total number of codes is

\(12\times20=240.\)

(d) For the code to be even, the last digit must be one of \(2,4,6,8\), so there are \(4\) choices for the last digit.

After that, the first three digits can be chosen from the remaining \(8\), then \(7\), then \(6\) numbers.

Therefore the number of even codes is

\(4\times8\times7\times6=1344.\)