Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.2 Arc Length and Speed - Exercises - Page 611: 15

$$4\sqrt{10} $$

Since speed is given by \begin{align*} \frac{d s}{d t}&=\sqrt{x^{\prime}(t)^{2}+y^{\prime}(t)^{2}}\\ &=\sqrt{9t^4+4t^2 } \end{align*} Then \begin{align*} \frac{d s}{d t}\bigg|_{t= 2} &=\sqrt{9(2)^4+4(2)^2 } \\ &= 4\sqrt{10} \end{align*}