We are asked to solve two problems. The first problem is to evaluate the expression $\frac{3}{4} - \frac{1}{6}$. The second problem is to order the following fractions from smallest to largest: $\frac{5}{6}$, $\frac{4}{9}$, and $\frac{2}{3}$.

1. Problem Description

We are asked to solve two problems.

The first problem is to evaluate the expression $\frac{3}{4} - \frac{1}{6}$.

The second problem is to order the following fractions from smallest to largest: $\frac{5}{6}$, $\frac{4}{9}$, and $\frac{2}{3}$.

2. Solution Steps

First, let's solve $\frac{3}{4} - \frac{1}{6}$.

To subtract these two fractions, we need to find a common denominator. The least common multiple of 4 and 6 is

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2.

$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$

$\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}$

So, $\frac{3}{4} - \frac{1}{6} = \frac{9}{12} - \frac{2}{12} = \frac{9-2}{12} = \frac{7}{12}$.

Next, let's order the fractions $\frac{5}{6}$, $\frac{4}{9}$, and $\frac{2}{3}$ from smallest to largest.

To compare these fractions, we need to find a common denominator. The least common multiple of 6, 9, and 3 is

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8.

$\frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}$

$\frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18}$

$\frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18}$

Now we can compare the fractions: $\frac{8}{18} < \frac{12}{18} < \frac{15}{18}$.

Therefore, $\frac{4}{9} < \frac{2}{3} < \frac{5}{6}$.

3. Final Answer

The first problem's answer is $\frac{7}{12}$.

The second problem's answer is $\frac{4}{9}, \frac{2}{3}, \frac{5}{6}$.