Step 1 :Given that the full recipe requires \(\frac{4}{5}\) cups of water, we need to find out how much water is needed for \(\frac{1}{12}\) of the recipe.
Step 2 :To do this, we multiply the amount of water needed for the full recipe by the fraction of the recipe we want to make.
Step 3 :\(\frac{4}{5} \times \frac{1}{12} = \frac{1}{15}\)
Step 4 :Final Answer: The amount of water needed to make \(\frac{1}{12}\) th of the recipe is \(\boxed{\frac{1}{15}}\) cups.