SELECT service_id FROM language_services WHERE language_id = 1 OR language_id = 2 GROUP BY service_id HAVING COUNT(*) = 2
Or...
WHERE lanaguage_id IN (1,2) GROUP BY service_id HAVING COUNT(*) = 2
If you always look at 2 languages, you can do this with unions, but the consolidated version is easier to adapt to different numbers of language_ids. (Add OR or add an item to the IN list and change COUNT(*) = 2 to COUNT(*) = 3 , etc. Etc.).
Remember, however, that this is very small. And with this table structure, you can't do anything about it.
EDIT Connection example for two languages
SELECT lang1.service_id FROM language_services AS lang1 INNER JOIN language_services AS lang2 ON lang1.service_id = lang2.service_id WHERE lang1.language_id = 1 AND lang2.language_id = 2
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