What is this? I'm unsure of the finer points. Those who reject Darwinian evolution, how old do they say the world is?
This site, which has a more protestant leaning, should give you a run down on this view: https://www.gotquestions.org/old-earth-creationism.html Also check out their article linked there on young earth and theistic evolutionist views.
The "young earth" models all trace back to the work of James Ussher (who was Archbishop of Armagh for about 30 years in the 17th century). He used what were considered reliable fixed time points to establish a chronology working back into the OT. From there he slavishly followed the Masoretic text until he arrived at 4004 B.C. as the date of creation. No one uses his particular figures anymore but his methodology is still used by the YECs to make their own chronologies of time. Most of them are now using the rounded figure of 6,400 years as the approximate age of the Earth. For more information on that method, look up "Answers in Genesis." They are a creationist group that sends out lecturers, publishes, and runs several young earth themed attractions here in the US.