There's really two different approaches to 432 Hz . One is simply tuning everything down 8 cents but still remaining in equal temperament so the realtionship between pitches is still the same as 440 just slightly lower , that is just a matter of taste and pretty inconvenient to others who are in 440 .
But if you have an instrument tuned to just intonation or pythagorean tuning it is possible to arrive at A being 432 Hz but with the relationship to other pitches changed . Not everyone's cup of tea but it can take the edge off some major thirds if you find them a bit "off in equal temperament . Doesn't apply to string players or singers who can sing what the feel is most appropriate as they are not forced into the tyranny of an equal tempered machine like a keyboard , or the enforced pitching of frets where bending of single notes is difficult within a chord .