Which of the following molecules does not show stereo isomerism?

Stereoisomerism includes geometric (E/Z) isomerism and optical isomerism. We check each compound for the presence of a chiral centre or a restricted-rotation unit (such as a double bond) with two different groups on each carbon.

3,4-Dimethylhex-3-ene: the double bond is between C3 and C4. Carbon 3 bears a methyl group and an ethyl group ($$\text{CH}_2\text{CH}_3$$); carbon 4 bears a methyl group and an ethyl group. Both carbons carry two different substituents, so E/Z isomerism is possible.

3-Methylhex-1-ene: carbon 3 is bonded to H, $$\text{CH}_3$$, $$\text{CH}=\text{CH}_2$$, and $$\text{CH}_2\text{CH}_2\text{CH}_3$$ — four different groups, making it a chiral centre. This compound shows optical isomerism.

3-Ethylhex-3-ene has the structure $$\text{CH}_3\text{CH}_2\text{C}(=\text{CHCH}_2\text{CH}_2\text{CH}_3)\text{CH}_2\text{CH}_3$$. Carbon 3 carries two identical ethyl groups ($$\text{CH}_2\text{CH}_3$$). Since one of the doubly-bonded carbons has two identical substituents, E/Z isomerism is not possible. There is also no chiral centre in the molecule. Therefore, 3-ethylhex-3-ene does not show stereoisomerism.

4-Methylhex-1-ene: carbon 4 is bonded to H, $$\text{CH}_3$$, $$\text{CH}_2\text{CH}=\text{CH}_2$$, and $$\text{CH}_2\text{CH}_3$$ — four different groups, making it a chiral centre capable of optical isomerism.

The answer is option (3): 3-Ethylhex-3-ene.