By the equality rule for rational numbers, $\frac{a}{b} = \frac{c}{d}$ if $ad = bc$. For $\frac{2}{3}$ and $\frac{4}{6}$, $ad = 2 \times 6 = 12$ and $bc = 3 \times 4 = 12$. Since $ad = bc$, the numbers are equal.

For $\frac{5}{4}$ and $\frac{10}{8}$, $ad = 5 \times 8 = 40$ and $bc = 4 \times 10 = 40$. Since $ad = bc$, the numbers are equal.

For $-\frac{3}{5}$ and $-\frac{6}{10}$, $ad = -3 \times 10 = -30$ and $bc = 5 \times -6 = -30$. Since $ad = bc$, the numbers are equal.

For $\frac{9}{3}$ and $3$ (written as $\frac{3}{1}$), $ad = 9 \times 1 = 9$ and $bc = 3 \times 3 = 9$. Since $ad = bc$, the numbers are equal.