We have the following function
[tex]D(t)=2.5\sin\frac{\pi t}{6}+12[/tex]The maximum and minimum of that function happens when sin(x) = 1 or sin(x) = -1, respectively.
Then let's find the maximum, that happens when the sin value is 1
[tex]\begin{gathered} \begin{equation*} D(t)=2.5\sin\frac{\pi t}{6}+12 \end{equation*} \\ \\ D(t)=2.5\cdot1+12 \\ \\ D(t)=2.5+12 \\ \\ D(t)=14.5 \end{gathered}[/tex]And the minimum, when sin value is -1
[tex]\begin{gathered} \begin{equation*} D(t)=2.5\sin\frac{\pi t}{6}+12 \end{equation*} \\ \\ D(t)=2.5\cdot(-1)+12 \\ \\ D(t)=-2.5+12 \\ \\ D(t)=9.5 \end{gathered}[/tex]Then the least: 9.5 hours; greatest: 14.5 hours.