12 teams. Six east, six west. Let's see?
East: Giants, Browns, Steelers, Eagles, Redskins, Cardinals
West: Bears, Rams, 49ers, Colts, Packers, Lions
Now, that I’ve looked it up, you’re correct that there were 12 teams in 1951 (still, much fewer than the 32 of today) and one was the New York Yanks (nee Bulldogs) who disbanded a year later and the first Dallas Texans were created to replace them. They later moved to Baltimore and became the Colts.
Cleveland, Los Angeles and San Francisco had just been added from the disbanded All-American Football Conference (AAFC) so it was an eight or nine-team league in the late 1940s.