Product of the addition of 1 eq. bromine to 1-methylcyclohexa-1,4-diene
You misunderstood what hyperconjugation is. It occurs when the electrons in a $\ce{C-H}$ $\sigma$-bond are shared with an adjacent atom's empty or partially filled $\mathrm{p}$-orbital, giving the species an extended molecular orbital and thereby stabilizing it. This means that hyperconjugation doesn't really come into play until bromine is added across one of the double bonds. Let's consider the two possible intermediates:

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The first one is a tertiary carbocation, and the second is a secondary carbocation. The first intermediate is more stable due to the hyperconjugative effects of the methyl group, and will require less energy to form than the second. This means the reaction will occur much faster at the more substituted double bond, and is why that is the major product.