To determine the number of teaspoons of cocoa needed for nine cups of milk, we can use the given ratio of cocoa to milk, which is 2 teaspoons of cocoa for every 1 cup of milk.
We calculate the amount of cocoa needed as follows:
\[ \text{Cocoa needed} = \text{Cups of milk} \times \text{Teaspoons of cocoa per cup} \]
Substituting the values:
\[ \text{Cocoa needed} = 9 \text{ cups} \times 2 \text{ teaspoons/cup} = 18 \text{ teaspoons} \]
Therefore, for nine cups of milk, you need 18 teaspoons of cocoa.