**Correct option is (B) 3 2/3**

Let sum of scored runs on first 5 balls in the last over is x.

After hitting 6 on last ball of the over, the mean score becomes 4 runs per ball.

\(\therefore\) \(\frac{x+6}6=4\)

\(\Rightarrow\) \(\frac{x}6+1=4\)

\(\Rightarrow\) \(\frac{x}6=4-1=3\)

\(\Rightarrow\) x = 6 \(\times\) 3 = 18

Hence, the sum of scored runs on first 5 balls in the last over is 18.

Given that Sachin scored 4 runs on last ball.

\(\therefore\) Mean \(=\frac{18+4}6\)

\(=\frac{22}6\) \(=3\frac46\)

\(=3\frac23\)

Hence, the mean score per ball in that over is \(3\frac23.\)