The multiplicative inverse of a quantity - [tex]x[/tex], say - denoted by [tex]x^{*}[/tex], must satisfy the following:
[tex]xx^{*} = 1[/tex],
giving
[tex]x^{*} = \frac{1}{x}[/tex].
So in this case that [tex]x = \frac{4}{3a}[/tex],
[tex]x^{*} = \frac{1}{(\frac{4}{3a})} = \frac{3a}{4}[/tex]
