jmc

Since $|-4+ti|=\sqrt{(-4{)}^2+t^2}=\sqrt{t^2+16}$, the equation $|-4+ti|=2\sqrt{13}$ tells us that $\sqrt{t^2+16}=2\sqrt{13}$. Squaring both sides gives $t^2+16=52$, so $t^2=36$. Since we want the positive value of $t$, we have $t=\boxed{6}$.