Sum of items = Mean x Number of items.

Mean = 17.6

Number of girls in the class = t

Sum of the ages of girls = 17.6 x t = 17.6t

When the girls where dismissed, the sum of the ages reduced to 17.6t - (16 + 19 + 20 + 17) and the number of girls reduced to t - 4

Note: 4 girls were dismissed.

New sum of ages = 17.6t - (16 + 19 + 20 + 17)

New sum of ages = 17.6t - 72

New number of girls = t - 4

New mean = $\frac{\mathrm{17.6t\; -\; 72}}{\mathrm{t\; -\; 4}}$

The new mean age of girls in the class became 0.2 less than the original mean.

Original mean = 17.6

New mean = 17.6 - 0.2 = 17.4

$\frac{\mathrm{17.6t\; -\; 72}}{\mathrm{t\; -\; 4}}$ = 17.4

Get rid of the fraction by multiplying both sides by the denominator t - 4

$\frac{\mathrm{17.6t\; -\; 72}}{\mathrm{t\; -\; 4}}$ x (t - 4) = 17.4 x (t - 4)

17.6t - 72 = 17.4t - 69.6

17.6t - 17.4t = 72 - 69.6

0.2t = 2.4

Divide both sides by 0.2

t = $\frac{2.4}{0.2}$ = 12