CREATE TABLE checkins
(
    date_in DateTime,
    date_out DateTime,
    age Int32,
    sex String,
    date_day Date MATERIALIZED toDate(date_in)
) ENGINE = MergeTree(date_day, date_in, 8192)

INSERT INTO checkins VALUES
    (toDateTime('2018-01-01 08:30:00'), toDateTime('2018-01-01 16:30:00'), 32, 'M'),
    (toDateTime('2018-01-01 09:30:00'), toDateTime('2018-01-01 10:30:00'), 28, 'M'),
    (toDateTime('2018-01-01 10:15:00'), toDateTime('2018-01-01 10:45:00'), 30, 'M'),
    (toDateTime('2018-01-01 11:30:00'), toDateTime('2018-01-01 11:45:00'), 35, 'M'),
    (toDateTime('2018-01-01 14:30:00'), toDateTime('2018-01-01 17:30:00'), 25, 'F');

SELECT count(*), instant
FROM
(
    SELECT arrayJoin([toDateTime('2018-01-01 10:00:00'), toDateTime('2018-01-01 12:00:00'), toDateTime('2018-01-01 14:00:00'), toDateTime('2018-01-01 16:00:00')] AS tabinstants) AS instant
    FROM checkins
    WHERE (date_in < instant) AND (date_out > instant)
)
GROUP BY instant
ORDER BY instant ASC

┌─count()─┬─────────────instant─┐
│       2 │ 2018-01-01 10:00:00 │
│       1 │ 2018-01-01 12:00:00 │
│       1 │ 2018-01-01 14:00:00 │
│       2 │ 2018-01-01 16:00:00 │
└─────────┴─────────────────────┘

┌─count()─┬─────────────instant─┐
│       3 │ 2018-01-01 10:00:00 │
│       1 │ 2018-01-01 12:00:00 │
│       2 │ 2018-01-01 14:00:00 │
│       2 │ 2018-01-01 16:00:00 │
└─────────┴─────────────────────┘