I hold Duke stock which offered Spectra energy which became Enbridge. How do I calculate the basis of the Enbridge, which I sold?

To start, you have to know the cost basis for each lot of Duke Energy you owned prior to the Spectra Energy spinoff.   Next, you have to allocate that cost basis between Duke and Spectra.  For information on how to do make that allocation, see: https://www.duke-energy.com//_/media/pdfs/our-company/investors/spectra-tax-info.pdf

Once you have determined the basis of the shares of Spectra Energy you owned, you can use the following Exchange Calculator to determine your Enbridge basis: http://www.spectraenergypartners.com/Investors/Stock-Information/Exchange-Calculator.aspx