The correct option is Only four.

Explanation

A country's number of time zones is determined by its longitudinal spread and the inclusion of overseas territories, dependencies, and island possessions. Countries with geographically dispersed territories across wide longitudinal ranges tend to observe multiple time zones.

United Kingdom — More than four time zones: Correct
The United Kingdom, along with its Crown Dependencies and Overseas Territories, spans multiple time zones. These include territories such as the Falkland Islands, South Georgia, British Indian Ocean Territory, Pitcairn Islands, and others scattered across the Atlantic, Indian, and Pacific Oceans. In total, the UK observes approximately 9 time zones when all its territories are included, which is well in excess of four.
Denmark — More than four time zones: Correct
Denmark, through its constituent territories of Greenland and the Faroe Islands, spans multiple time zones. Greenland alone covers four time zones due to its vast east–west longitudinal extent. Denmark as a whole therefore observes more than four time zones.
New Zealand — More than four time zones: Correct
New Zealand, including its overseas territories and associated states such as the Tokelau Islands, Niue, Cook Islands, and the Chatham Islands, spans several time zones. The total number of time zones observed exceeds four when all New Zealand's dependencies are accounted for.
Australia — More than four time zones: Correct
Australia observes multiple standard and daylight saving time zones across its mainland states and territories, including Australian Central Western Standard Time (ACWST) which is a UTC+8:45 offset — a rare fractional zone. Including its external territories such as Christmas Island, Cocos (Keeling) Islands, Norfolk Island, and others, Australia spans more than four time zones.
Brazil — More than four time zones: Incorrect
Despite being the largest country in South America with considerable longitudinal spread, Brazil observes four time zones — including the standard zones for its mainland regions and the zone applicable to Fernando de Noronha island. Brazil does not exceed four time zones, making it the country that does not satisfy the given condition.

Thus, four of the five listed countries — the United Kingdom, Denmark, New Zealand, and Australia — have more than four time zones. Brazil, with exactly four time zones, does not meet this criterion.

Key Takeaway: Brazil observes exactly four time zones and thus does not exceed four; the remaining four countries — UK, Denmark, New Zealand, and Australia — each observe more than four time zones when their overseas territories and dependencies are included.