First, convert both planes to the same form. The second plane \(4x + 2y + 4z + 5 = 0\) can be written as \(2x + y + 2z + \frac{5}{2} = 0\) by dividing by 2. Now both planes have the form \(2x + y + 2z = d\). For the first plane, \(d_1 = 8\) and for the second, \(d_2 = -\frac{5}{2}\). The distance formula between parallel planes is \(d = \frac{|d_1 - d_2|}{\sqrt{a^2 + b^2 + c^2}}\) where \(a=2, b=1, c=2\). Thus \(d = \frac{|8 - (-\frac{5}{2})|}{\sqrt{4+1+4}} = \frac{|\frac{21}{2}|}{3} = \frac{21}{6} = \frac{7}{2}\).