The number of x's is at least L.
For simplicity let L = 4.
The required minimal Finite Automata is
For L = 4, we have 5 States. Similarly For no. of x's is at least L, We have (L + 1) States.
Note: Here both minimal DFA and minimal NFA have same states.
An interesting question would be: The no. of states in Minimal finite automata such that no. of x's is exactly L.
Here minimal NFA will have (L + 1) states.
Minimal DFA will have (L + 2) states.
Therefore, Minimal Finite automata will have (L + 1) states.