Question : For random variables $\displaystyle X,Y$ and $\displaystyle Z$, it is given that
$\displaystyle Cov(X,Y) = a$ and $\displaystyle Cov(X,Z) = c$
Obtain $\displaystyle Cov(X,Y+Z)$
You have got to start reading and understanding your class notes and textbook! Many of the questions you are posting are done using basic definitions and formulae. MHF is not a service for doing all your homework.
This question is nothing more than applying a basic formula:
Cov(X, Y + Z) = Cov(X, Y) + Cov(X, Z).
See here: Covariance - Wikipedia, the free encyclopedia