6. Combine: $$ \left(\frac{1}{3} x^{2}-\frac{5}{6} x+\frac{3}{4}\right)-\left(\frac{7}{12} x^{2}+\frac{1}{2} x-\frac{2}{3}\right) $$

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To combine the given expressions:

$$
\left(\frac{1}{3} x^{2} - \frac{5}{6} x + \frac{3}{4}\right) - \left(\frac{7}{12} x^{2} + \frac{1}{2} x - \frac{2}{3}\right)
$$

**Step 1: Distribute the Negative Sign**

Subtract the second polynomial by distributing the negative sign:

$$
\frac{1}{3} x^{2} - \frac{5}{6} x + \frac{3}{4} - \frac{7}{12} x^{2} - \frac{1}{2} x + \frac{2}{3}
$$

**Step 2: Combine Like Terms**

1. **Combine $$ x^2 $$ terms:**
   $$
   \frac{1}{3} x^{2} - \frac{7}{12} x^{2} = \left(\frac{4}{12} - \frac{7}{12}\right) x^{2} = -\frac{3}{12} x^{2} = -\frac{1}{4} x^{2}
   $$

2. **Combine $$ x $$ terms:**
   $$
   -\frac{5}{6} x - \frac{1}{2} x = \left(-\frac{5}{6} - \frac{3}{6}\right) x = -\frac{8}{6} x = -\frac{4}{3} x
   $$

3. **Combine constant terms:**
   $$
   \frac{3}{4} + \frac{2}{3} = \frac{9}{12} + \frac{8}{12} = \frac{17}{12}
   $$

**Step 3: Write the Final Combined Expression**

Putting it all together:

$$
-\frac{1}{4} x^{2} - \frac{4}{3} x + \frac{17}{12}
$$

**Final Answer:**

$$
-\frac{1}{4}x^{2}\ -\ \frac{4}{3}\,x\ +\ \frac{17}{12}
$$
$$ -\frac{1}{4}x^{2} - \frac{4}{3}x + \frac{17}{12} $$

Combine:

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