To find the equilibrium price and quantity, we need to set the demand equal to the supply and solve for the equilibrium price (P).
Demand (D) = Supply (S)

\(20 - \frac{1}{2}P = 8 + \frac{1}{4}P\)

Now, let's solve for P:

\(20 - 8 = \frac{1}{2}P + \frac{1}{4}P\)

\(12 = \frac{3}{4}P\)

To find P, we multiply both sides by \(\frac{4}{3}\):

\(P = \frac{12 \times 4}{3} = 16\)

Now that we have the equilibrium price, we can find the equilibrium quantity by substituting P into either the demand or supply equation.

Let's use the demand equation:

\(D = 20 - \frac{1}{2}P\)

\(Q = 20 - \frac{1}{2}(16)\)

\(Q = 20 - 8\)

\(Q = 12\)

So, the equilibrium price (P) is 16 and the equilibrium quantity (Q) is 12.

Therefore, the correct answer is P = 16, Q = 12