I am designing the style for a book. I want a 8.5"x11" page and will need about 6 styles. I’d like to base them on the same style 8.5x11 page, so that I only have one place to change when I print this as a 6x9 paperback. The “Inherit from” line is always greyed out! I am running LO6.2.5, but have tried this on the RC of 6.3 as well.
Please don’t answer to yourself, edit your question.
Yes, inheritance isn’t available for page styles. See tdf#41316, which is the tracker for this issue.
If Inheritance isn’t implemented why have an “inheritance drop-down”. Remove the drop-down until you have implemented it. It does seem a pain for those of us that live in the letter-size, rather than the A4-size parts of the world to have to tweak the page size in several places for the default to the only size paper that we can buy. ;=}
Is it an enhancement request? then you, of course, know that there’s a proper place to file those, while here they are off-topic; also you surely know that on this site, Answer is meant to answer the original question, not to comment on someone’s answer… I can’t think that someone doesn’t read the site’s usage rules 
Also the part
for those of us that live in the letter-size, rather than the A4-size parts of the world to have to tweak the page size in several places
sounds like having wrong locale settings (set to a locale which uses A4-sized stuff), because in LibreOffice, when you set your locale to a Letter-sized location, the defaults are set to Letter; and also - one could of course use templates fine-tuned to whatever settings one wants.