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To solve this problem, we need to find the equilibrium price (P) and equilibrium quantity (Q) by setting the demand function equal to the supply function.

### Given:
- Demand function: \( Q_d = -2P + 12 \)
- Supply function: \( Q_s = 2P - 4 \)

### Steps to find the equilibrium:

1. **Equilibrium Condition**: 
   At equilibrium, the quantity demanded (\(Q_d\)) equals the quantity supplied (\(Q_s\)):

   \[
   Q_d = Q_s
   \]

   So,

   \[
   -2P + 12 = 2P - 4
   \]

2. **Solve for P**:
   To find the equilibrium price, let's solve the equation:

   \[
   -2P + 12 = 2P - 4
   \]

   Add \(2P\) to both sides:

   \[
   12 = 4P - 4
   \]

   Add 4 to both sides:

   \[
   16 = 4P
   \]

   Divide both sides by 4:

   \[
   P = 4
   \]

   So, the equilibrium price is \( P = 4 \).

3. **Find the equilibrium quantity**:
   Now, substitute \( P = 4 \) into either the demand or supply equation. Let’s use the supply function:

   \[
   Q_s = 2P - 4
   \]

   Substituting \( P = 4 \):

   \[
   Q_s = 2(4) - 4 = 8 - 4 = 4
   \]

   So, the equilibrium quantity is \( Q = 4 \).

### Conclusion:
- The equilibrium price is \( P = 4 \).
- The equilibrium quantity is \( Q = 4 \).

Would you like a detailed graph of this equilibrium situation? If you have any questions, feel free to ask.

---

### Related Questions:
1. What happens to the equilibrium if the demand function shifts to \( Q_d = -3P + 15 \)?
2. How do changes in supply (e.g., \( Q_s = 3P - 6 \)) affect equilibrium?
3. Can you describe the effect of a price ceiling set below the equilibrium price?
4. How is consumer surplus calculated at equilibrium?
5. What is the role of elasticity in determining the steepness of the supply and demand curves?

### Tip:
Equilibrium occurs where the supply and demand curves intersect. It's useful to graph the functions to visualize how price and quantity adjust to reach this point.

Diketahui fungsi permintaan dari suatu barang adalah Qd = -2P + 12 dan fungsi penawarannya adalah Qs = 2P - 4. Carilah keseimbangan pasar dari barang tersebut dan gambarkan.

Learn how to find the market equilibrium from the given demand function Qd = -2P + 12 and supply function Qs = 2P - 4. This step-by-step solution includes solving linear equations to determine the equilibrium price and quantity.

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