Final answer:
Alice can embroider 18 different types of design on the 3 pieces of cloth.
Step-by-step explanation:
Alice has 3 pieces of cloth, and she embroiders different types of design on each piece of cloth so that each design covers 1/6 of the cloth. Since there are 3 pieces of cloth and 6 equal parts in each cloth, Alice can embroider a total of 3 x 6 = 18 different types of design on the 3 pieces of cloth.