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2 Answers

Volume = Area x "How tall the shoebox is" . Therefore the answer is Volume / Area, that is 546 cubic inches / 84 sq. inches, yielding 6.5 inches tall.
 
The shoebox is 6.5 inches tall.
Volume = length * width * height = 546 cubic inches
 
Length * width = 84 sq. inches
 
Height = (546 cubic in)/(84 sq. in) = 6.5 inches