Simplify: \( 2 \sqrt{15} \cdot 4 \sqrt{30} \)

To simplify the expression \( 2 \sqrt{15} \cdot 4 \sqrt{30} \), first multiply the coefficients: \( 2 \cdot 4 = 8 \). Next, multiply the square roots: \( \sqrt{15} \cdot \sqrt{30} = \sqrt{15 \cdot 30} = \sqrt{450} \). Now, simplify \( \sqrt{450} \). We can break it down: \( 450 = 9 \cdot 50 = 9 \cdot (25 \cdot 2) = (3^2 \cdot 5^2 \cdot 2) \). So, \( \sqrt{450} = \sqrt{9 \cdot 50} = \sqrt{9} \cdot \sqrt{50} = 3 \cdot \sqrt{50} \). And since \( \sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2} \), we have: \( \sqrt{450} = 3 \cdot 5 \sqrt{2} = 15 \sqrt{2} \). Putting it all together: \( 2 \sqrt{15} \cdot 4 \sqrt{30} = 8 \cdot 15 \sqrt{2} = 120 \sqrt{2} \). Thus, the simplified expression is: \[ \boxed{120 \sqrt{2}} \]