Just like Australia, New Zealand and Canada have been self-governing countries within the British Commonweath since 1948. Remember, you're being quizzed on countries, not realms, here!
Please note the instructions. Territories of the United Kingdom like Gibraltar and the Falklands are subject to the jurisdiction of the UK, but do not form a part of it. Faroe Islands are a constituent country, not a territory, of the 3-country Kingdom of Denmark. If Greenland was close enough, it would be here, but it's 1464 km / 909 km away.
And then why Faroe islands? Its part of Denmark
If you put in Faroe islands you should also put in Greenland