To find out how many different ways four students can line up against a blackboard, we need to calculate the number of permutations of these four students.
When arranging \(\( n \)\) students in a line, the number of possible arrangements (permutations) can be found by using the factorial function, denoted as \(\( n! \)\). The factorial of a number \(\( n \)\) is the product of all positive integers less than or equal to \(\( n \)\).
For our problem, we have 4 students, so we need to find \(\( 4! \)\) (4 factorial):
\(\[ 4! = 4 \times 3 \times 2 \times 1 = 24 \]\)
Thus, the number of different ways four students can line up against a blackboard is \(\( 24 \)\).
Therefore, the correct answer is:
(D) 24
