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The correct answer is $14$. It's given that the equation $46=2a+2b$ gives the relationship between the side lengths $a$ and $b$ of a certain parallelogram. Substituting $9$ for $a$ in the given equation yields $46=2\left(9\right)+2b$, or $46=18+2b$. Subtracting $18$ from both sides of this equation yields $28=2b$. Dividing both sides of this equation by $2$ yields $14=b$. Therefore, if $a=9$, the value of $b$ is $14$.