Consider a right rectangular prism where the length is twice the width, and the height is 4 cm. If the width is represented as \( w \), express the volume of the prism in terms of \( w \).
The volume \( V \) of a rectangular prism is calculated using the formula \( V = l \times w \times h \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height.