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If a card is a face card and the coin lands on the head, then you win $\$6.$

If a card is a face card and the coin lands on tails, then you win $\$2.$

If a card is not a face card, then you lose $\$2.$

$$\begin{gathered} E\left(x\right)=\underset{}{∑\left[X×P\left(x\right)\right]} \\ E\left(x\right)=6×\frac{9}{13}+2×\frac{3}{13}-2×\frac{-20}{13} \\ E\left(x\right)=-\frac{8}{13} \end{gathered}$$

There is an Expected loss of$-8/13$.

If a card is a face card and the coin lands on the head, then you win $\$6.$

If a card is a face card and the coin lands on tails, then you win $\$2.$

If a card is not a face card, then you lose$\$2.$

This indicates that in long term there will be a loss because the probability of getting a loss is more than getting a profit. So, there will be a loss.

If a card is a face card and the coin lands on the head, then you win$\$6$.

If a card is a face card and the coin lands on tails, then you win $\$2.$

If a card is not a face card, then you lose$\$2.$

NO, I should not play this game as we have already seen in the above part that there is a higher probability of loss. So, we will not play this game.