Proving a Problem is in NP
Another way to show your problem is NP-complete is to show that a known NP-complete problem can be reduced to it in polynomial time.
E.g. The Hamiltonian Circuit problem is known to be NP-complete (find a cycle in a directed graph of n vertices that travels through each vertex exactly once and returns to the start).
Let’s prove (very informally) that TSP is NP-complete.