Here
\(\frac{4 quarts of Alcohol}{4 quarts of water}\)

we need to add water to above solution to make it equal to = \(\frac{3 parts of Alcohol}{5 parts of water}\)
Let w= quarts of water required

Total quarts of water = (4 + w)

Therefore we can re write as -

\(\frac{4 quarts of Alcohol}{(4 quarts of water + w)}\) = \(\frac{3 parts of Alcohol}{5 parts of water}\)(since we need to add w to make the ratio equal to 3/5)

or \(\frac{4}{(4+w)}\) =\(\frac{3}{5}\)

or w =\(\frac{8}{3}\)