To determine which fraction is equivalent to [tex]\(\frac{2}{3}\)[/tex], we need to find a fraction that, when simplified, results in [tex]\(\frac{2}{3}\)[/tex]. Here are the steps to verify:
1. Check [tex]\(\frac{3}{5}\)[/tex]:
- Simplify [tex]\(\frac{3}{5}\)[/tex]: This is already in its simplest form.
- Compare with [tex]\(\frac{2}{3}\)[/tex]: Clearly, [tex]\(\frac{3}{5}\)[/tex] does not simplify to [tex]\(\frac{2}{3}\)[/tex].
2. Check [tex]\(\frac{2}{6}\)[/tex]:
- Simplify [tex]\(\frac{2}{6}\)[/tex]: Divide the numerator and the denominator by their greatest common divisor, which is 2.
[tex]\[
\frac{2 \div 2}{6 \div 2} = \frac{1}{3}
\][/tex]
- Compare with [tex]\(\frac{2}{3}\)[/tex]: [tex]\(\frac{1}{3}\)[/tex] is not equal to [tex]\(\frac{2}{3}\)[/tex].
3. Check [tex]\(\frac{4}{6}\)[/tex]:
- Simplify [tex]\(\frac{4}{6}\)[/tex]: Divide the numerator and the denominator by their greatest common divisor, which is 2.
[tex]\[
\frac{4 \div 2}{6 \div 2} = \frac{2}{3}
\][/tex]
- Compare with [tex]\(\frac{2}{3}\)[/tex]: [tex]\(\frac{4}{6}\)[/tex] simplifies directly to [tex]\(\frac{2}{3}\)[/tex].
Thus, the fraction [tex]\(\frac{4}{6}\)[/tex] is equivalent to [tex]\(\frac{2}{3}\)[/tex].
So the correct choice is:
[tex]\[
\boxed{\frac{4}{6}}
\][/tex]
