Let's calculate the minimum amount Mr. William could have paid at the shop by taking into account the discounts available for buying one shirt and for buying three shirts.

If Mr. William buys one shirt, he gets a flat discount of 20%. The discounted price of one shirt would be:

$60 - 20% of $60 = $60 - $12 = $48

So, if Mr. William buys one shirt, he would pay $48.

If Mr. William buys three shirts, he can get them at the price of two shirts. The total cost for three shirts would be:

2 x $60 = $120

So, if Mr. William buys three shirts, he would pay $120.

Now, Mr. William bought a total of 10 shirts. To minimize the cost, he can buy three sets of three shirts (9 shirts in total) at the price of two sets of three shirts, and one additional shirt.

Total cost for 9 shirts (three sets of three shirts): 3 x $120 = $360
Total cost for 1 additional shirt: 1 x $48 = $48

Adding both costs:

$360 + $48 = $408

So, the minimum amount Mr. William could have paid at the shop is $408. Therefore, the correct answer is $408.