Structure of the compound whose `IUPAC` name is `3-`ethyl`-2-`hydroxy`-4-`methylhex`-3-`en`-5-`ynoic acid is

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Explanation

To derive the structure of the compound with the IUPAC name `3-ethyl-2-hydroxy-4-methylhex-3-en-5-ynoic acid`, we will follow a systematic approach step-by-step.

### Step 1: Identify the Parent Chain
The name indicates that the parent chain is "hex", which means it contains 6 carbon atoms.

**Hint:** Look for the prefix in the name (hex) to determine the number of carbon atoms in the main chain.

### Step 2: Draw the Parent Chain
Draw a straight chain of 6 carbon atoms and number them from 1 to 6.

```
C1 - C2 - C3 - C4 - C5 - C6
```

**Hint:** Number the carbon atoms sequentially from one end of the chain to the other.

### Step 3: Identify and Place the Functional Groups
1. **Carboxylic Acid Group (oic acid)**: The "oic acid" suffix indicates that there is a carboxylic acid group (-COOH) at the end of the chain. Since we have 6 carbons, this group will be on carbon 1.
2. **Hydroxy Group (2-hydroxy)**: The "2-hydroxy" indicates there is a hydroxyl group (-OH) on carbon 2.
3. **Ethyl Group (3-ethyl)**: The "3-ethyl" indicates there is an ethyl group (-CH2CH3) on carbon 3.
4. **Methyl Group (4-methyl)**: The "4-methyl" indicates there is a methyl group (-CH3) on carbon 4.
5. **Double Bond (hex-3-en)**: The "3-en" indicates a double bond between carbon 3 and carbon 4.
6. **Triple Bond (5-yne)**: The "5-yne" indicates a triple bond between carbon 5 and carbon 6.

**Hint:** Pay attention to the order of substituents and functional groups as indicated by the IUPAC name.

### Step 4: Add the Groups to the Structure
Now, we will add the identified groups to the carbon chain:

1. Place the carboxylic acid group (-COOH) on C1.
2. Place the hydroxyl group (-OH) on C2.
3. Place the ethyl group (-CH2CH3) on C3.
4. Place the methyl group (-CH3) on C4.
5. Indicate the double bond between C3 and C4.
6. Indicate the triple bond between C5 and C6.

The structure will look like this:

```
OH
|
C1 - C2 - C3 = C4 - C5 ≡ C6
| |
COOH CH3
|
CH2CH3
```

### Step 5: Complete the Valencies
Now, ensure that all carbon atoms have four bonds. Add hydrogen atoms where necessary to satisfy the tetravalency of carbon.

**Hint:** Each carbon should have four bonds total; add hydrogen atoms to balance the structure.

### Final Structure
The final structure of the compound is:

```
OH
|
C1 - C2 - C3 = C4 - C5 ≡ C6
| |
COOH CH3
|
CH2CH3
```

### Summary
The structure of the compound with the IUPAC name `3-ethyl-2-hydroxy-4-methylhex-3-en-5-ynoic acid` has been constructed by identifying the parent chain, placing the substituents and functional groups, and ensuring all valencies are satisfied.