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The correct answer is $\mathrm{2,048}$. The area $A$, in square inches, of a rectangle is equal to the product of its length $l$, in inches, and its width $w$, in inches, or $A=lw$. It's given that the rectangle has a length of $64$ inches and a width of $32$ inches. Substituting $64$ for $l$ and $32$ for $w$ in the equation $A=lw$ yields $A=\left(64\right)\left(32\right)$, or $A=\mathrm{2,048}$. Therefore, the area, in square inches, of the rectangle is $\mathrm{2,048}$.