The ratio of the side length is,
[tex]\frac{s}{l}=\frac{3}{4}[/tex]The ratio of side smaller diamone to side of larger diamond is always remain constant. So,
[tex]\begin{gathered} \frac{6}{l}=\frac{3}{4} \\ l=\frac{6\cdot4}{3} \\ =8 \end{gathered}[/tex]So length of the larger diamond is 8 inches.