Answer
$3024$ ways
Work Step by Step
If we want to choose $k$ elements out of $n$ regarding the order and not allowing repetition, we can do this with permutations:
$_{n}P_k=\frac{n!}{(n-k)!}$ ways.
In our case, we wish to seat 4 people into 9 seats. Since order matters, we use permutations:
$_{9}P_{4}=\frac{9!}{(9-4)!}=\frac{9!}{5!}=\frac{9*8*7*6*5!}{5!}=9\cdot8\cdot7\cdot6=3024$
