The correct answer is option 3, which states that extensive deserts occur in the Western Tropical Regions of Continents because of the effect of both offshore easterly trade winds and cold ocean currents.

Let`s dissect the other options to understand why they are incorrect:

Option 1 suggests that extensive deserts occur due to easterly trade winds. While easterly trade winds do exist in the Western Tropical Regions, they are not the sole reason for the occurrence of deserts.

Option 2 suggests that gold ocean currents flow along the western coasts, causing extensive deserts. However, there is no such thing as "gold ocean currents," and the presence of ocean currents does not directly result in the formation of deserts.

Option 4 states that the rate of exploration is greater along the western margin areas, leading to extensive deserts. However, exploration has no direct impact on the formation of deserts in the Western Tropical Regions.

Therefore, option 3 provides the most accurate explanation as it considers the combined effect of offshore easterly trade winds and cold ocean currents in the occurrence of extensive deserts in the Western Tropical Regions of Continents.