Section 1947.12 is the rent cap half of the Tenant Protection Act. Subdivision (a) says that over any 12-month period an owner of residential real property may not raise the gross rental rate by more than 5 percent plus the percentage change in the cost of living, or 10 percent, whichever of those two is lower. The comparison is made against the lowest gross rental rate charged for that unit at any time in the 12 months before the increase takes effect, and discounts or concessions the tenant accepted are excluded from that figure — so a landlord cannot manufacture headroom by discounting first. The same subdivision caps the number of increases: no more than two increments in any 12 months for a tenant who stays.
The cap follows the unit, not the tenant, only up to a point. Subdivision (b) is the part landlords rely on: when no tenant from the prior tenancy remains in lawful possession, the owner sets the initial rent for the new tenancy free of subdivision (a), and the cap then applies to increases after that. That is why the section restrains rent during a tenancy without controlling what a unit is advertised at once it is empty.
Subdivision (d) is where most disputes actually land, because it lists the housing this section does not reach: deed-restricted affordable housing, dormitories, housing already under a stricter local rent ordinance, housing issued a certificate of occupancy within the previous 15 years, single-family homes and condominiums separately alienable where the owner is not a REIT, corporation or corporate-member LLC and the required written exemption notice was given, and owner-occupied duplexes. The exemption notice has prescribed wording, which is why the question "is my building covered" is usually answered by reading the lease and the age of the building rather than by reading the cap itself. Working out coverage for a particular address, and what a landlord owes if an increase went over, is a matter for a lawyer or a local rent board.