grep -ro "pattern to find in files" "directory to recursively search" | grep -c "pattern to find in files"
This solution will count all occurrences even if there are multiple on one line.
-r recursively searches the directory
-o will "show only the part of a line matching PATTERN"
this is what splits up multiple occurences on a single line and makes grep print each match on a new line;
then pipe those newline-separated-results back into grep with -c to count the number of occurrences using the same pattern.