Imagine you owe ₹10 to four people. Your total balance is −₹40. That is 4 × (−10) = −40. A positive number of debts, each negative, totals negative. Easy.

Now imagine someone removes one of those debts from your books. You now owe one fewer debt. Your balance has changed by +₹10. That is (−1) × (−10) = +10. Subtracting a negative is adding.

Negative multiplication is, in a sense, the act of removing groups. Remove three groups of "owing four rupees," and you are richer by ₹12. (−3) × (−4) = +12.

Different language. Same idea. Same answer. Some students click with the proof; some click with the metaphor. Use whichever helps you explain it to the friend you sit next to.