[Rutherford]

A substance has the formula C₆H₈. 1mole of it reacts with 2moles of hydrogen. When 1mole of it reacts with 1 mole of bromine only one product is made without counting the optical isomers. Determine its structure.

I don't know how to do it with only the data given here. It has 2 bonds and it has to be cyclic. The answer is 1,3-cyclohexadiene, but why can't it be e.g. the compound attached here? It gives 1 product when reacting with bromine, too.

[discodermolide]

I suppose it could be that compound, in theory.
These are very unstable. I don't think the one you drew exists. If you make them you can coordinate them with an iron carbonyl which forms a pi-complex with the iron stabilising the cyclobutene. Done at low temperature.
See: http://en.wikipedia.org/wiki/Cyclobutadiene and
http://en.wikipedia.org/wiki/Cyclobutadieneiron_tricarbonyl

[Rutherford]

Theoretically possible-should be enough to make the answer wrong. Thanks for the explanation.

[Wastrel]

You'd get three products brominating.  If the methyls were trans, that might fulfill the criteria.

[curiouscat]

Theoretically possible-should be enough to make the answer wrong. Thanks for the explanation.

Not if it doesn't exist.

[Rutherford]

If I as a high school student get such a problem, I can't know whether such a compounds exist or not.

Wastrel-optical isomers aren't counted.

[Wastrel]

3 structural isomers.  Don't take the double bonds literally.

[Rutherford]

Then it should be 3 isomers for a mixture of Z/E, Z/Z and E/E, but only 1 compound should be the answer.
Anyway this look like a conjugated diene so the 1,4-addition should be possible, too. Then the conjugated dienes are excluded leaving only 1,3-cyclohexadiene.