1. **State the problem:** Simplify the expressions $6\sqrt{35}$ and $3\sqrt{13} \times 2\sqrt{13}$.\n\n2. **Simplify $6\sqrt{35}$:** This expression is already simplified because $35$ is $5 \times 7$, and neither 5 nor 7 is a perfect square. So, $6\sqrt{35}$ remains as is.\n\n3. **Simplify $3\sqrt{13} \times 2\sqrt{13}$:** Use the property of radicals and multiplication: $a\sqrt{b} \times c\sqrt{d} = (a \times c) \sqrt{b \times d}$.\n\n4. Apply the formula: $$3\sqrt{13} \times 2\sqrt{13} = (3 \times 2) \sqrt{13 \times 13} = 6 \sqrt{169}.$$\n\n5. Since $\sqrt{169} = 13$, substitute back: $$6 \times 13 = 78.$$\n\n**Final answers:**\n- $6\sqrt{35}$ (cannot be simplified further)\n- $3\sqrt{13} \times 2\sqrt{13} = 78$