How many possible syllogistic patterns are produced by four figures and four proposition forms?

In traditional categorical syllogistic, there are 256 possible syllogistic forms.1

This total is derived from the combination of moods and figures:

• Moods: Because each of the three propositions in a syllogism (two premises and one conclusion) can take one of four forms (A, E, I, or O), there are $4\times 4\times 4=64$ possible moods.21
• Figures: There are four figures, which are defined by the arrangement of the middle term within the premises.21

By multiplying the 64 possible moods by the four figures, one arrives at 256 possible syllogistic patterns. One of the primary objectives of syllogistic logic has been to analyze these patterns to distinguish the valid forms from the invalid ones.1