Tech Guide question regarding Enterprise vs Equity Value

I came across a question/answer in a technical interview guide and I can't seem to understand the logic/wording of the answer.

Q: Would you be calculating Enterprise Value or Equity Value when using a multiple based on free cash flow or EBITDA?

A: EBITDA and free cash flow represent cash flows that are available to repay holders of company's debt and equity, so a multiple based on one of those two metrics would describe the value of the firm to all investors. A multiple such as P/E ratio, based on earnings alone, represents the amount available to common shareholders after all expenses are paid, so if you used this multiple, you would be calculating the value of the firm's equity.

Perhaps I'm just confused by the wording of the answer, but surely a multiple based on EBITDA would be calculated using the Enterprise Value? If EBITDA represents a cash flow that is capable of repaying equity and debt, surely then we would need to account for the firm's debt by using the enterprise value instead of pure equity value?

Thanks guys.