Let's solve the equation step by step:

\[
\frac{1}{6}d + \frac{2}{3} = \frac{1}{4}(d + 2)
\]

### Step 1: Eliminate the fraction on the right-hand side
Distribute the \(\frac{1}{4}\) on the right side:

\[
\frac{1}{6}d + \frac{2}{3} = \frac{1}{4}d + \frac{1}{2}
\]

### Step 2: Eliminate fractions by finding a common denominator
The least common denominator (LCD) for 6, 3, 4, and 2 is 12. Multiply the entire equation by 12 to eliminate the fractions:

\[
12 \times \left(\frac{1}{6}d + \frac{2}{3}\right) = 12 \times \left(\frac{1}{4}d + \frac{1}{2}\right)
\]

This gives:

\[
2d + 8 = 3d + 6
\]

### Step 3: Simplify the equation
Move all the terms involving \(d\) to one side and the constants to the other side:

\[
2d - 3d = 6 - 8
\]

This simplifies to:

\[
-d = -2
\]

### Step 4: Solve for \(d\)

\[
d = 2
\]

So, the solution to the equation is \(d = 2\).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the least common denominator for fractions?
2. How do you handle equations with multiple fractions?
3. What happens if the fractions have different denominators?
4. How do you distribute fractions across parentheses?
5. What is the purpose of simplifying equations step by step?

**Tip**: Always check your solution by substituting it back into the original equation!

Learn how to solve the linear equation 1/6d + 2/3 = 1/4(d + 2) with a detailed step-by-step explanation. This problem covers important algebraic concepts, including solving equations with fractions and eliminating fractions using the least common denominator. Suitable for students in Grades 7-9.

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