People remember one number and apply it everywhere. OSHA has at least four, and each belongs to a particular kind of work.
Construction, generally: 6 feet. Each employee on a walking/working surface with an unprotected side or edge 6 feet or more above a lower level must be protected by guardrail systems, safety net systems, or personal fall arrest systems (29 CFR 1926.501(b)(1)). The same 6-foot threshold runs through the rest of 1926.501(b) — leading edges, holes, formwork, ramps, excavations, roofing — with the specific options varying by situation. Residential construction keeps the 6-foot trigger, with a written fall protection plan allowed only where the employer can demonstrate that conventional systems are infeasible or create a greater hazard (29 CFR 1926.501(b)(13)).
Scaffolds: 10 feet. Each employee on a scaffold more than 10 feet above a lower level must be protected from falling, with the type of protection set by scaffold type (29 CFR 1926.451(g)(1)); for scaffolds not otherwise specified, that means personal fall arrest systems or guardrail systems (29 CFR 1926.451(g)(1)(vii)).
Steel erection: 15 feet. Each employee engaged in steel erection on a walking/working surface with an unprotected side or edge more than 15 feet above a lower level must be protected by guardrail, safety net, personal fall arrest, positioning device, or fall restraint systems, subject to the exceptions in paragraph (a)(3) (29 CFR 1926.760(a)(1)).
General industry: 4 feet. Outside construction, each employee on a walking-working surface with an unprotected side or edge 4 feet or more above a lower level must be protected (29 CFR 1910.28(b)(1)(i)). A maintenance crew working on an existing building's mezzanine is in Part 1910; the contractor building the mezzanine is in Part 1926.
Two things follow. First, the question is never only "how high" but "under which standard," which depends on whether the activity is construction, and on the equipment involved. Second, each of these is a minimum; nothing stops an employer from protecting at a lower height, and many do.