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 $w$.