The problem provides the following inequalities:

• $3 < a < 6$
• $6 < b < 8$

You are asked to find all possible values for $b - a$.

Step 1: Understand the range of $b - a$

The range for $a$ is between 3 and 6, and the range for $b$ is between 6 and 8. To find the possible values of $b - a$, you subtract $a$ from $b$.

Step 2: Analyze boundary values

The maximum value of $b - a$ will occur when $b$ is at its maximum (close to 8) and $a$ is at its minimum (close to 3):

$b - a = 8 - 3 = 5$

The minimum value of $b - a$ will occur when $b$ is at its minimum (close to 6) and $a$ is at its maximum (close to 6):

$b - a = 6 - 6 = 0$

Step 3: Conclusion

Thus, the possible values of $b - a$ range from $0$ to $5$.

$0 < b - a < 5$

Would you like more details or further clarification?

Here are 5 related questions:

1. What happens to the value of $b - a$ if we change the boundaries for $a$?
2. How can we interpret the range of $b - a$ geometrically?
3. Can $b - a$ ever be negative based on the given conditions?
4. How would the solution change if the inequalities were strict or non-strict (e.g., $\leq$ instead of $<$)?
5. What if $b$ had a smaller maximum range, how would that affect the outcome?

Tip: Always examine the boundary values carefully, as they often provide critical information for solving inequality-based problems.