Calculate the signal's average power
A signal either has finite energy, finite power or even infinite power. If it has finite energy, it will have zero average power, according to your definition
$$P_x=\lim_{T_0\rightarrow\infty}\frac{1}{T_0}\int_{-\frac{T_0}{2}}^{\frac{T_0}{2}}|x(t)|^2dt.$$

Knowing that the sincs are orthogonal to each other, as well as the cos function, the average power is given by

$$P_x=P(2)+P(2\cos(2\pi f_0t))+P(\operatorname{sinc})$$

where $P(...)$ is the power of the components in brackets. The sinc function has finite energy, hence it has zero power on average. Hence, we have 

$$P_x=P(2)+P(2\cos(2\pi f_0 t)$$
with
$$P(2)=4$$
and $$P(2\cos(2\pi f_0 t)=2^2\cdot\frac{1}{2}=2.$$

Therefore, the overall power is given by

$$P_x=6.$$

For the calculation of the $\cos$, consider
$$P_{\cos}=\frac{1}{T}\int_{0}^{T}\cos^2(2\pi t/T)dt=\frac{1}{2}$$