Explanation:

- Option 1: 1956

The government first recognized the need for family planning around this time and started a national family planning program. However, a department in the ministry was not formalized then.

- Option 2: 1986

By this time, the focus on family planning had shifted towards more comprehensive health and welfare, but it wasn't the year a dedicated department was established.

- Option 3: 1976

Several new policies were introduced during this period related to population control, but the department wasn't established in this year.

- Option 4: 1966

This is the correct year when a dedicated department for family planning was created in the Ministry of Health.