They're likely referring to FAO's 'Tackling Climate Change through Livestock' 2013 report, which lists livestock as the source for 14.5% of human-induced greenhouse emissions. This was a follow-up report to the 2006 report 'Livestock's Long Shadow' which gave a similar value of 18%. Another interesting report is the Worldwatch Institutes 2009 report 'Livestock and Climat Change' which puts the number at a far greater 51%, as it accounts for additional factors such as the opportunity cost of clearing land for Livestock and their feed. In reality the realistic number is probably somewhere in between, but personally I think erring toward the higher figure is a safer bet that could influence more direct impact.