Первый пришедший в голову вариант:
SELECT user_id
FROM some_table
WHERE num IN (878, 925, 242)
GROUP BY user_id
HAVING COUNT(DISTINCT num) = 3 -- 3 количество вариантов
;
MySQL fiddle
Вариант с JOIN:
SELECT some_table.user_id
FROM some_table
JOIN some_table st1 ON st1.user_id = some_table.user_id AND st1.num = 925
JOIN some_table st2 ON st2.user_id = some_table.user_id AND st2.num = 242
WHERE some_table.num = 878
;
MariaDB fiddle
Вариант с GROUP_CONCAT (номера должны быть отсортированы):
SELECT user_id, GROUP_CONCAT(DISTINCT num ORDER BY num)
FROM some_table
WHERE num IN (878,925,242)
GROUP BY user_id
HAVING GROUP_CONCAT(DISTINCT num) = '242,878,925'
;
MySQL 8.0 Fiddle