1. **State the problem:** Simplify the expression $3\sqrt{13} \times 2\sqrt{13}$.\n\n2. **Recall the multiplication rule for radicals:** When multiplying expressions with square roots, multiply the coefficients (numbers outside the roots) and multiply the numbers inside the roots separately.\n\n3. **Apply the rule:**\n$$3\sqrt{13} \times 2\sqrt{13} = (3 \times 2)(\sqrt{13} \times \sqrt{13})$$\n\n4. **Simplify the coefficients:**\n$$3 \times 2 = 6$$\n\n5. **Simplify the radicals:**\n$$\sqrt{13} \times \sqrt{13} = \sqrt{13 \times 13} = \sqrt{169}$$\n\n6. **Evaluate the square root:**\n$$\sqrt{169} = 13$$\n\n7. **Combine the results:**\n$$6 \times 13 = 78$$\n\n**Final answer:** $78$