Simplify $$ \frac{3}{4}+\frac{2}{3}(9 x+6)+4 x+3 \frac{1}{4} $$

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To simplify the expression:

$$
\frac{3}{4} + \frac{2}{3}(9x + 6) + 4x + 3 \frac{1}{4}
$$

**Step 1: Distribute $$\frac{2}{3}$$**
$$
\frac{2}{3}(9x + 6) = \frac{2}{3} \times 9x + \frac{2}{3} \times 6 = 6x + 4
$$

**Step 2: Convert Mixed Number to Improper Fraction**
$$
3 \frac{1}{4} = \frac{13}{4}
$$

**Step 3: Combine All Terms**
$$
\frac{3}{4} + 6x + 4 + 4x + \frac{13}{4}
$$

**Step 4: Combine Like Terms**
- Combine the $$x$$ terms:
  $$
  6x + 4x = 10x
  $$
- Combine the constant terms:
  $$
  \frac{3}{4} + 4 + \frac{13}{4} = \frac{3}{4} + \frac{16}{4} + \frac{13}{4} = \frac{32}{4} = 8
  $$

**Final Simplified Expression:**
$$
10x + 8
$$

**Alternatively, Factored Form:**
$$
2(5x + 4)
$$

**Answer:**
After simplifying, the expression is equal to ten x plus eight. In symbols,

10 x + 8
The simplified expression is $$10x + 8$$.

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