Identify the principal functional group

The compound contains:

• an alcohol group, $-OH$
• a double bond
• an ethyl substituent

In IUPAC nomenclature, the alcohol has higher priority than the double bond, so the parent name must use the suffix -ol.

Choose the parent ring and numbering

The parent ring is cyclopentene/cyclopentanol framework, i.e. a five-membered ring.

Since $-OH$ is the principal functional group, numbering must start from the carbon bearing the $-OH$ group.

So the carbon with $-OH$ gets locant 1.

Assign positions to the double bond and substituent

After giving $-OH$ locant 1, number the ring in the direction that gives the double bond the lowest possible locant.

This gives:

• $-OH$ at carbon $1$
• double bond at carbon $2$  so parent becomes cyclopent-2-en-1-ol
• ethyl substituent at carbon $4$

Write the complete name

Therefore, the correct IUPAC name is:

$\boxed{4\text{-Ethylcyclopent-2-en-1-ol}}$

Check the options

• A: $1$-Ethylcyclopent-$2$-en-$3$-ol  incorrect, because the $-OH$ group should get locant $1$.
• B: $4$-Ethylcyclopent-$2$-en-$1$-ol  correct.
• C: $1$-Ethyl-$3$-hydroxycyclopent-$2$-ene  incorrect, because alcohol should be written as suffix -ol, not prefix hydroxy, when it is the principal group.
• D: $4$-Ethyl-$1$-hydroxycyclopent-$2$-ene  incorrect for the same reason.

Comparison with stored correct answer

My derived answer is B, which matches the stored correct answer.