I4.1 If $f(t)=2-\frac{t}{3}$, and $f(a)=-4$, find $a$.
I4.2 If $a+9=12 Q+r$, where $Q, r$ are integers and $0<r<12$, find $r$.
I4.3 $x, y$ are real numbers. If $x+y=r$ and $M$ is the maximum value of $x y$, find $M$.
I4.4 If $w$ is a real number and $2^{2 w}-2^{w}-\frac{8}{9} M=0$, find $w$.
$\begin{array}{l}f(a)=2-\frac{a}{3}=-4 \\ \Rightarrow a=18 \\ 18+9=27=12 \times 2+3=12 Q+r \\ r=3 \\ x+y=3 \\ \Rightarrow y=3-x \\ x y=x(3-x)=3 x-x^{2}=-(x-1.5)^{2}+2.25 \\ M=2.25=\frac{9}{4} \\ 2^{2 w}-2^{w}-\frac{8}{9} \cdot \frac{9}{4}=0 \\ \Rightarrow\left(2^{w}\right)^{2}-2^{w}-2=0 \\ \left(2^{w}+1\right)\left(2^{w}-2\right)=0 \\ \Rightarrow w=1\end{array}$