1. **State the problem:** Add the mixed number $12 \frac{3}{4}$ and $0$. 2. **Formula and rules:** Adding zero to any number leaves the number unchanged. So, $a + 0 = a$. 3. **Intermediate work:** $$12 \frac{3}{4} + 0 = 12 \frac{3}{4}$$ 4. **Explanation:** Since adding zero does not change the value, the sum remains $12 \frac{3}{4}$. **Final answer:** $$12 \frac{3}{4}$$