In four years Kay will be twice as old as Gordon. Four years after that Shaun will be twice as old as Kay. Four years after that Shaun will be three times as old as Gordon. How many years old is Shaun now?
1. Let the current ages of Kay, Gordon, and Shaun be denoted by \( K \), \( G \), and \( S \) respectively.

2. According to the problem, in four years, Kay will be twice as old as Gordon:
   \[
   K + 4 = 2(G + 4)
   \]
   Simplifying this equation:
   \[
   K + 4 = 2G + 8 \implies K = 2G + 4
   \]

3. Four years after that (i.e., eight years from now), Shaun will be twice as old as Kay:
   \[
   S + 8 = 2(K + 8)
   \]
   Substituting \( K = 2G + 4 \) into the equation:
   \[
   S + 8 = 2((2G + 4) + 8) \implies S + 8 = 2(2G + 12) \implies S + 8 = 4G + 24 \implies S = 4G + 16
   \]

4. Four years after that (i.e., twelve years from now), Shaun will be three times as old as Gordon:
   \[
   S + 12 = 3(G + 12)
   \]
   Substituting \( S = 4G + 16 \) into the equation:
   \[
   4G + 16 + 12 = 3(G + 12) \implies 4G + 28 = 3G + 36 \implies 4G - 3G = 36 - 28 \implies G = 8
   \]

5. Now, substituting \( G = 8 \) back into the equation for \( S \):
   \[
   S = 4G + 16 \implies S = 4(8) + 16 \implies S = 32 + 16 \implies S = 48
   \]

The final answer is \(\boxed{48}\)