jmc

Since $|-4+ti|=\sqrt{(-4{)}^2+t^2}=\sqrt{t^2+16}$, the equation $|-4+ti|=6$ tells us that $\sqrt{t^2+16}=6$. Squaring both sides gives $t^2+16=36$, so $t^2=20$. Since we want the positive value of $t$, we have $t=\boxed{2\sqrt{5}}$.