The selling price of a refrigerator, is $866.40. If the markup is 20% of the dealers cost, what is the dealers cost of the refrigerator.

Let's assume the dealer's cost of the refrigerator is x.

The markup is 20% of the dealer's cost, which is 0.20x.
Therefore, the selling price is the sum of the dealer's cost and the markup: x + 0.20x = 866.40
Combining like terms: 1.20x = 866.40
Dividing both sides by 1.20: x = 866.40 / 1.20 = $722.
Therefore, the dealer's cost of the refrigerator is $722. Answer: \boxed{722}.