The FAQ refers to "pagebreak hints". I can't find any mention of these by searching (for "[page-breaking] hints" and various other things). What are pagebreak hints and how does one use them?
The answers to What are penalties and which ones are defined? can be a guide, but perhaps it's better to show the LaTeX way for suggesting page breaks.
The commands for this are
\nopagebreak. They can be used both in a paragraph or between paragraphs (that is, with a blank line before and after them). When in the body of a paragraph they refer to a possible page break after the line where the commands finally appear in the typeset output.
Each one takes an optional argument, a number from 0 to 4, and the unadorned commands are equivalent to specify 4.
\pagebreakmeans "this is a good place for breaking a page, but don't take it too seriously"
\pagebreakmeans "this is a rather nice place for breaking a page"
\pagebreakmeans "this is a nice place for breaking a page"
\pagebreakmeans "this is a very nice place for breaking a page"
\pagebreak) means "break a page here"
\nopagebreakmeans "this is a bad place for breaking a page, but don't take it too seriously"
\nopagebreakmeans "this is a rather bad place for breaking a page"
\nopagebreakmeans "this is a bad place for breaking a page"
\nopagebreakmeans "this is a very bad place for breaking a page"
\nopagebreak) means "don't break a page here"
\nopagebreak is completely equivalent: the "don't take it too seriously" means just this. The sense is "this is a place where breaking is feasible", which between paragraphs or after a line is usually the case (unless it would create a widow or club line). So they can be used as a reminder that we might have something to do with page breaks there during the final revision.
Such commands should be used only during the final revision of the document, when the text is in its final form and we need to correct possible bad page breaks; in this situation we do know where to place them, if we have to use them in the body of a paragraph, because paragraph are broken into lines at an earlier stage of processing.
When a new edition of the document is prepared, then all
\nopagebreak commands added in the final revision should be removed, because the pagination will probably be different and a forced page break can spoil the new edition.