That's documented in the bash manual under Shell Parameter Expansion:
${parameter%word}
${parameter%%word}
The word is expanded to produce a pattern and matched according to the rules described below (see Pattern Matching). If the pattern matches a trailing portion of the expanded value of parameter, then the result of the expansion is the value of parameter with the shortest matching pattern (the % case) or the longest matching pattern (the %% case) deleted. If parameter is @ or *, the pattern removal operation is applied to each positional parameter in turn, and the expansion is the resultant list. If parameter is an array variable subscripted with @ or *, the pattern removal operation is applied to each member of the array in turn, and the expansion is the resultant list.
In other words, ${f%????} is the value of $f with the four last characters deleted.
You could also write ${f:0:-4}, which is perhaps a bit clearer.