This question refers to a market in which quantity demanded is given by $q = a - bp$ and quantity supplied by $q = c + dp$.
In this market, an increase in the parameter $a$ would:
a. increase quantity and decrease price.
b. decrease both price and quantity.
c. increase both price and quantity.
d. increase price and decrease quantity.
One of the tenets of economics is that in equilibrium $$Supply=Demand$$ Both supply and demand are functions of price. So in order to find an equilibrium we need find a price that satisfy the above equation. If supply and demand equations are well-behaved (i.e., supply equation increasing in price and demand equation decreasing in price) then there is a unique equilibrium price such that demand=supply.
So in your case $$ a-bp = c+dp$$
Solving this equation for $p$ you obtain $$ p = \frac{a-c}{b+d} $$ Note that the price needs to be non-negative and finite, which imposes restrictions on the parameters. Assuming that $b,d>0$ so that demand and supply functions are well behaved, we have requirement that $a-c>0$.
We can now answer your question. Differentiating $p$ wrt $a$ we obtain $$\frac{\partial p}{\partial a} = \frac{1}{b+d}>0$$
Therefore, equilibrium price increases following an increase in $a$. Moreover, since equilibrium $p$ increases, the supply function implies that the equilibrium quantity will increase as well.
So answer C is correct: Both equilibrium price and equilibrium quantity will increase.