In the image, we have two angles that form a straight line, which means they are supplementary. Supplementary angles sum up to $180^\circ$.

The angles given are: $(8d + 4)^\circ \quad \text{and} \quad (6d + 8)^\circ.$

Since these angles form a straight line, we can set up the equation: $(8d + 4) + (6d + 8) = 180.$

Now, let's solve for $d$:

1. Combine like terms: $8d + 6d + 4 + 8 = 180.$ $14d + 12 = 180.$

2. Subtract 12 from both sides: $14d = 180 - 12.$ $14d = 168.$

3. Divide both sides by 14: $d = \frac{168}{14}.$ $d = 12.$

Thus, the value of $d$ is $12$.

Would you like a detailed explanation of any step?

Here are some related questions you might consider:

1. What is the measure of each angle when $d = 12$?
2. How do you verify if two angles are supplementary?
3. What is the general formula for supplementary angles?
4. Can angles that sum to $180^\circ$ always be supplementary?
5. How can you apply this concept to angles in geometric shapes?

Tip: When dealing with linear angles, remember that the sum will always be $180^\circ$, which helps in setting up the equation.