The answer is cuántas.
Step-by-step explanation:
The best word to complete the question is cuántas. Hence, the whole sentence would be: ¿Cuántas cucharadas de azúcar necesito agregar a la mezcla?
Cuántas is an interrogative word fulfilling the function of a determiner since it is modifying the noun "cucharadas". In English, we would say HOW MANY.