The internal energy (U), pressure (P) and volume (V) of an ideal gas are related as U=3PV+4.

$Given : U=3PV+4$

$\text{using ideal gas equation,} PV=nRT$

$\begin{array}{l}\Rightarrow U=3nRT+4\\ \Rightarrow dU=3nRdT\\ \Rightarrow n{C}_{V}dT=3nRdT\\ \Rightarrow C_V=3R\\ \Rightarrow \frac{fR}{2}=3R\\ \Rightarrow f=6\\ \text{ Hence, gas is polyatomic }\end{array}$