As　a　direction　selection　in　the　direction　distance　function　(DDF),　endogenous　DDF　can　accurately　reflect　the　numerical　characteristics　of　inputs/outputs,　but　it　is　difficult　to　effectively　popularize.　And　it　is　also　difficult　to　effectively　combine　with　reality.　To　solve　those　problems,　this　paper　introduces　slack　variables　to　construct　a　new　endogenous　direction-setting　mechanism,　which　makes　the　endogenous　model　have　the　conditions　to　be　popularized.　Based　on　the　original　endogenous　DDF,　we　consider　environmental　concern,　economic　concern,　coordinated　development,　and　priority　development,　and　then　construct　six　new　extended　DDF　models　with　slack　variables.　Based　on　priority　development,　we　further　propose　six　new　extended　DDF　models.　These　new　extended　models　can　not　only　realize　the　complete　internalization　of　direction　determination　but　also　overcome　the　limitations　of　traditional　endogenous　models.　Combined　with　the　actual　case,　the　emission　reduction　potential　of　different　areas　is　revealed,　and　the　improved　path　is　proposed.　The　results　show　that　the　new　extended　DDF　models　effectively　reflect　the　different　development　modes　of　carbon　emissions,　and　different　development　modes　have　a　significant　impact　on　emission　reduction　potential.　In　addition,　compared　with　economic　concern　and　priority　development,　coordinated　development　and　environmental　concern　are　most　beneficial　to　carbon　emission　reduction,　but　the　development　mode　of　environmental　concern　can　better　reveal　the　improved　path　of　environmental　development.　©　2025　by　the　authors.