Simplified path. The puzzle showed the main steps; the full route is being checked.
Late Latin
coquina
‘A kitchen’
into Old English
Old English
cycene
‘A kitchen’
became Middle English
Middle English
kichene
‘A kitchen’
became English
English
kitchen
‘The cooking room’
The story of kitchen
Kitchen came into Old English from the Latin cooking family. Coquina, cycene, and kichene show how its form changed on the way to the modern spelling. The room kept a stable function while its name changed shape.
These are selected stages, not every spelling or intermediary. The story identifies omitted links; older forms did not all disappear at once.