When the plans say
VENT INTERSECTION MUST BE
AT LEAST 6" ABOVE RIM OF
HIGHEST FIXTURE SERVED
In the case of a bathtub....does that mean above the rim of the bathtub or where the drain is?
The idea is that if the drain pipe becomes clogged and water backs up, it will flood over the rim of the highest fixture before it flows (and potentially clogs)
horizontal vent pipes of other fixtures. For example: Assume you tied the tub vent horizontally into the vertical sink vent above the sink drain tee/trap, but below the rim of the sink. If the sink drain becomes clogged, the water will flow down the tub vent before it ever overflows the sink rim; which, in turn, could cause drainage and venting issues at the tub.
Typically the laundry box will be the highest point on any floor level that has a laundry connection, so if that's the case, the vent intersection should be 6" above that. If there's no laundry on that floor, then the highest fixture would typically be a lavatory/sink.