Statistics and Probability: JEE Main 2024 Mathematics question

If the mean of the following probability distribution of a radam variable $\mathrm{X}$ : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-baqh{text-align:center;vertical-align:top} $\mathrm{X}$ 0 2 4 6 8 $\mathrm{P(X)}$ $a$ $2a$ $a+b$ $2b$ $3b$ is $\frac{46}{9}$, then the variance of the distribution is