Mean of 30 marks must be reduced from 6.6 to 5.5 while SD must increase from 2.3 to 4.2.
Multiplying each number by n changes SD by n (Since SD = $\sum_i{(x_i-\mu)}^2$). So, we can make the SD change from 2.3 to 4.2 by multiplying each term by 4.2/2.3. This will also change the mean from 6.6 to 12.05.
Now, subtracting a constant from each term makes the mean reduce by that same constant. (since $\mu = \frac{\sum_i{x_i}}{n}$). So, to reduce the mean from 12.05 to 5.5 we should subtract 6.55 from each term. (Subtracting a constant from each term won't affect the standard deviation as mean and each term change by the same amount and hence also won't change).
So, our given value 8.5 becomes 8.5 * 4.2 / 2.3 = 15.52 for adjusting SD, and then becomes 15.52 - 6.55 = 8.97 when adjusted for mean.