1. **State the problem:** We have a vector $\mathbf{v} = \langle 12, 8 \rangle$ and a scalar $k$ such that $k\mathbf{v} = \langle 9, 6 \rangle$. We need to find the scalar $k$. 2. **Recall the scalar multiplication rule:** Multiplying a vector by a scalar multiplies each component of the vector by that scalar. So, $$k \mathbf{v} = k \langle 12, 8 \rangle = \langle 12k, 8k \rangle$$ 3. **Set up equations from components:** Since $k\mathbf{v} = \langle 9, 6 \rangle$, we have $$12k = 9 \quad \text{and} \quad 8k = 6$$ 4. **Solve for $k$ from the first component:** $$k = \frac{9}{12} = \frac{3}{4}$$ 5. **Check $k$ with the second component:** $$8k = 6 \implies k = \frac{6}{8} = \frac{3}{4}$$ 6. **Confirm both components give the same $k$:** Both equal $\frac{3}{4}$, so $k = \frac{3}{4}$. 7. **Answer:** The scalar $k$ is $\boxed{\frac{3}{4}}$, which corresponds to option A.