Let's solve the equation step by step:

Given equation:
\[
\frac{x + 6}{10} + \frac{x - 4}{15} = \frac{x + 2}{6}
\]

### Step 1: Find a common denominator.
The denominators are 10, 15, and 6. The least common denominator (LCD) of these numbers is 30.

### Step 2: Rewrite each fraction with the LCD.
- \(\frac{x + 6}{10} = \frac{3(x + 6)}{30} = \frac{3x + 18}{30}\)
- \(\frac{x - 4}{15} = \frac{2(x - 4)}{30} = \frac{2x - 8}{30}\)
- \(\frac{x + 2}{6} = \frac{5(x + 2)}{30} = \frac{5x + 10}{30}\)

### Step 3: Combine the left-hand side.
\[
\frac{3x + 18}{30} + \frac{2x - 8}{30} = \frac{(3x + 18) + (2x - 8)}{30} = \frac{5x + 10}{30}
\]

### Step 4: Set both sides of the equation equal.
\[
\frac{5x + 10}{30} = \frac{5x + 10}{30}
\]

### Step 5: Simplify the equation.
Since both sides are the same, this equation is an **identity**, meaning it is true for all values of \(x\).

### Final Answer:
The solution is that **all real numbers** are solutions, or simply:
\[
x \in \mathbb{R}
\]

Do you want more details on any of the steps, or have any questions?

Here are some related questions for further practice:
1. Solve \(\frac{x+5}{8} + \frac{x-3}{12} = \frac{2x+1}{6}\).
2. Solve \(2x + 3 = 5x - 4\).
3. Simplify \(\frac{x+2}{4} + \frac{x-1}{3} = \frac{5x+7}{12}\).
4. Solve for \(x\) in \(\frac{4x+1}{5} = \frac{x-2}{3}\).
5. Solve \(\frac{x+6}{15} + \frac{2x-4}{30} = \frac{x+1}{10}\).

**Tip:** Always look for a common denominator when working with equations that involve fractions.

This step-by-step guide shows how to solve the fractional linear equation x + 6/10 + x - 4/15 = x + 2/6. It covers important algebra concepts, including combining fractions using the least common denominator (LCD) and understanding identity equations. Suitable for students in Grades 6-8.

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