To determine which fraction is equivalent to [tex]\(\frac{1}{6}\)[/tex], let's compare each given option with [tex]\(\frac{1}{6}\)[/tex].
First, simplify the fractions and compare their values.
1. Option A: [tex]\(\frac{3}{8}\)[/tex]
No simplification is needed here. So, [tex]\(\frac{3}{8}\)[/tex].
2. Option B: [tex]\(\frac{2}{8}\)[/tex]
Simplify [tex]\(\frac{2}{8}\)[/tex]:
[tex]\[
\frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4}
\][/tex]
3. Option C: [tex]\(\frac{3}{24}\)[/tex]
Simplify [tex]\(\frac{3}{24}\)[/tex]:
[tex]\[
\frac{3}{24} = \frac{3 \div 3}{24 \div 3} = \frac{1}{8}
\][/tex]
4. Option D: [tex]\(\frac{4}{24}\)[/tex]
Simplify [tex]\(\frac{4}{24}\)[/tex]:
[tex]\[
\frac{4}{24} = \frac{4 \div 4}{24 \div 4} = \frac{1}{6}
\][/tex]
After simplification, we see that only Option D, [tex]\(\frac{4}{24}\)[/tex], is equivalent to [tex]\(\frac{1}{6}\)[/tex].
So, the answer is [tex]\( \boxed{4} \)[/tex].
