Sure! Let’s solve the two problems step-by-step.

### Bài 1: Solving equations

**a)** Solve the system:
\[
\begin{cases}
3x + 2y = 6 \\
2x - 2y = 14
\end{cases}
\]

To solve this, we can use the substitution or elimination method. Here, we can multiply the second equation by 1 to simplify:

1. From the first equation, express \(y\):
\[
2y = 6 - 3x \implies y = \frac{6 - 3x}{2}
\]

2. Substitute \(y\) into the second equation:
\[
2x - 2\left(\frac{6 - 3x}{2}\right) = 14
\]
\[
2x - (6 - 3x) = 14 \implies 2x - 6 + 3x = 14
\]
\[
5x - 6 = 14 \implies 5x = 20 \implies x = 4
\]

3. Substitute \(x\) back into the first equation to find \(y\):
\[
3(4) + 2y = 6 \implies 12 + 2y = 6 \implies 2y = -6 \implies y = -3
\]

So, the solution is \(x = 4\), \(y = -3\).

---

**b)** Solve the equation:
\[
x(x−2) - 3x + 6 = 0
\]

Expanding the equation:
\[
x^2 - 2x - 3x + 6 = 0 \implies x^2 - 5x + 6 = 0
\]

Now, factor it:
\[
(x - 2)(x - 3) = 0
\]

So, \(x = 2\) or \(x = 3\).

---

### Bài 2: Solving the word problems

**1)** Let's denote the price of the book before the discount as \(P\).

After applying the discount of 10%:
\[
\text{New price} = P - 0.10P = 0.90P
\]

You have:
\[
0.90P = 172 \implies P = \frac{172}{0.90} \approx 191.11 \text{ dong}
\]

The discount amount will be:
\[
P - 0.90P = 0.10P = 17.2 \text{ dong}
\]

---

**2)** Let’s denote the distance from A to B as \(D\).

The person moves from A to B at a speed of \(15 \text{ km/h}\) and returns at \(10 \text{ km/h}\). The time taken for this round trip can be calculated as follows:

1. Time from A to B:
\[
t_1 = \frac{D}{15}
\]

2. Time from B to A:
\[
t_2 = \frac{D}{10}
\]

The total time:
\[
t_1 + t_2 = 1 \text{ hour}
\]

So,
\[
\frac{D}{15} + \frac{D}{10} = 1
\]

To solve, find a common denominator (30):
\[
\frac{2D}{30} + \frac{3D}{30} = 1
\]
\[
\frac{5D}{30} = 1 \implies 5D = 30 \implies D = 6 \text{ km}
\]

### Summary:
- For Bài 1: \(x = 4\), \(y = -3\) in part a; \(x = 2\) or \(x = 3\) in part b.
- For Bài 2: The original book price is about \(191.11\) dong, and the distance \(D\) from A to B is \(6\) km.