For the best, most optimized solution, we first need to clarify the vocab you used here; it looks like you showed us two separate tables, not databases; are both of these tables (buildings and suites) contained within the same database?
If they are, and assuming one table is named 'buildings' and the other 'suites,' this query should give you what you want:
SELECT Suite_no, Rate, building_name
FROM suites s
LEFT JOIN buildings b
USING (building_id)
The syntax of the query was constructed with the assumption that you were using MySQL as your DBMS; mileage may vary with other servers.