The correct answer is option 4: 1, 2, and 3.

Let`s analyze each option to better understand why this is the correct answer:

Option 1: This option states that the remoteness of the American continent and the lack of good roads were reasons for the defeat of the British during the American War of Independence. This is correct because the distance between Britain and America made it difficult for the British forces to effectively communicate, transport troops and supplies, and maintain control over the colonies.

Option 2: This option states that the failure of the British authorities to rally the loyalist Americans was a reason for their defeat. This is correct because many Americans remained loyal to the British crown during the war, but the British were unable to effectively mobilize and gain support from these loyalists.

Option 3: This option states that the Americans benefited from the extraordinary military leadership of George Washington. This is correct because Washington was a skilled strategist and leader, who played a crucial role in leading the American forces to victory against the British.

Option 4: This option includes all three correct reasons stated above, making it the correct answer.

Therefore, option 4: 1, 2, and 3 is the correct answer.