If P = 2Qs + 2 represents market supply for a competitive industry and market demand is given by Qd = 21 - 1/2p, what is the equilibrium price...

In a competitive market, markets will clear, so supply will equal demand. Because firms have no power to adjust prices, they won't be able to maximize profit by adjusting price; instead, they will simply have to produce and sell goods up to the point where price is equal to marginal cost. Put another way, their marginal revenue is the demand curve (unlike in the case of monopoly or oligopoly), because if they try to price above marginal cost another firm will just undercut them.

We're given supply and demand equations:
P = 2Q_s + 2
Q_d = 21 - (1/2)P

The simplest way to solve is to start by isolating P on one side in each equation:
P = 2Q_s + 2
P = 42 - 2Q_d

Now use the fact that supply equals demand so Q_s = Q_d = Q.
P = 2 Q + 2
P = 42 - 2 Q

Since P = P, we can set the two equations equal:
2 Q + 2 = 42 - 2 Q

Solve for Q:
4Q = 40
Q = 10

Plug this back into the other equations (do both to make sure we didn't make a mistake):
P = 2 Q + 2 = 2(10) + 2 = 22
P = 42 - 2 Q = 42 - 2(10) = 22

Thus, the equilibrium price is $22 and the equilibrium quantity is 10 units of the good. This is an efficient equilibrium because the market is competitive.