You can observe many arrays in a supermarket such as cans on the shelves. This may be interpreted as a 4x6 array with four rows and 6 cans in each row or as a 6x4 array with six columns and 4 cans in each column. The following problem illustrates the use of the array interpretation of multiplication. Another interpretation that relates to the array model is the area model. The answer can be easily found from Fig.
Multiplication is also related to the Cartesian product of two sets.
Let us treat it from mathematical point of view as a set of four shapes. Formally a Cartesian product of any two sets is defined as a third set containing all different pairs of elements created by taking one element from the first set and one element from the second set. You can see the outcome of this operation represents the set of all shapes from the first set paired with all colors from the second set. All together 20 elements of the third set that differ by shape, color or both, shape and color. The number of elements of the third set can be obtained by multiplication of the number of elements in the first set by the number of elements in the second set.