The answer to this depends on exactly how literally you are taking this question. The tariff itself does not have to be greater than or equal to the autarky price in the country. However, the price with the tariff included does have to be. So if you think this question really is asking about the tariff itself, the correct answer is “False.”
The tariff itself does not have to be higher than the autarky price. Let us use an example to illustrate. Let us imagine that the price of a good is $8 under free trade and the autarky price is $10. A prohibitive tariff would not need to be $10 on the item. Instead, it simply has to ensure that the price of the item will rise above $10. Therefore, a tariff of $2 or more on the item will be prohibitive because it will raise the price of the item to the autarky price in the importing country.
So, this statement is false if we think that it really refers to the tariff itself. There is no need for a $10 tariff in this case because that would do more than enough to raise the price to the autarky level and destroy the incentive to import.