To determine the proper order from least to greatest for the fractions \( \frac{2}{3}, \frac{7}{6}, \frac{1}{8}, \frac{9}{10} \), let's go through a step-by-step comparison of their values.
1. Compare \( \frac{2}{3} \) and other fractions:
- \( \frac{2}{3} \approx 0.6667 \)
2. Compare \( \frac{7}{6} \) and other fractions:
- \( \frac{7}{6} \approx 1.1667 \)
- Clearly \( \frac{7}{6} > \frac{2}{3} \)
3. Compare \( \frac{1}{8} \) and other fractions:
- \( \frac{1}{8} = 0.125 \)
- Clearly \( \frac{1}{8} < \frac{2}{3} \) and \( \frac{1}{8} < \frac{7}{6} \)
4. Compare \( \frac{9}{10} \) and other fractions:
- \( \frac{9}{10} = 0.9 \)
- Clearly \( \frac{9}{10} > \frac{2}{3} \) but \( \frac{9}{10} < \frac{7}{6} \)
Thus, arranging these values from least to greatest, we have:
- \( \frac{1}{8} \)
- \( \frac{2}{3} \)
- \( \frac{9}{10} \)
- \( \frac{7}{6} \)
Hence, the proper order from least to greatest is:
[tex]\[ \frac{1}{8}, \frac{2}{3}, \frac{9}{10}, \frac{7}{6} \][/tex]
So, the correct answer is [tex]\( \boxed{B} \)[/tex].
