Which of the following is closest to $$ \frac{4}{3\pi}$$?

Incorrect.
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When you ballpark this answer choice, you get
>$$\displaystyle \sqrt{\frac{2}{3}} = \frac{\sqrt{2}}{\sqrt{3}} \approx \frac{1.4 }{1.7}$$.
Expand both the numerator and denominator by 10 to see this more clearly:
>$$\displaystyle \frac{1.4}{ 1.7} = \frac{14}{17}$$.
This is clearly more than $$\frac{1}{2}$$ ($$\frac{1}{2} = \frac{8.5}{17}$$). Since your target is slightly smaller than 0.5, check the other answer choices for a closer match.

Incorrect.
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When you ballpark this answer choice, you get
>$$\sqrt{3} -1 \approx 1.7-1 = 0.7$$.
This answer choice is greater than 0.5. Since your target is slightly _smaller_ than 0.5, check the other answer choices for a closer match.

Correct.
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When you ballpark this answer choice, you get
>$$\sqrt{2} -1 \approx 1.4-1 = 0.4$$.
This is slightly smaller than 0.5. All other answer choices are not in the right __Ballpark__, so this is the right answer choice.

$$\sqrt{2}-1$$

$$\sqrt{3} - 1$$

$$\sqrt{\frac{2}{3}}$$