Check if this works. It should generate a count of events per month, including months with no events. If it works then it's a trivial matter to use it as a table source for a query returning your output:
SELECT
safetyevent,
c.[Month],
[Rows] = COUNT(*)
FROM SafetyEventTable si
RIGHT OUTER JOIN (VALUES (1),(2),(3),(4),(5),(6),(7),(8),(9),(10),(11),(12)) c ([Month])
ON c.[Month] = MONTH(si.[Date])
GROUP BY safetyevent, c.[Month]
For fast, accurate and documented assistance in answering your questions, please read this article.
Understanding and using APPLY, (I) and (II) Paul White
Hidden RBAR: Triangular Joins / The "Numbers" or "Tally" Table: What it is and how it replaces a loop Jeff Moden