The reading for the 大 part is actually the on'yomi reading you learned when learning this kanji. Since 大 has two on'yomi readings, here's a mnemonic to help you remember which one to use:
When something's great and important, you'd better wear a tie (たい) for it. No showing up without a tie to anything that's a big deal, okay?
It’s not a big deal.
She is such a great woman.
Being the president of McDonald’s would be a big deal.