Step 1:

Since the solution is to be kept between $68^{\circ}$ and $77^{\circ}$ F

We have that, $68 < F <77$

Substituting for $F= \large\frac{9}{5} $$C +32$

We get $68 < \large\frac{9}{5}$$c +32 < 77$

Step 2:

Subtracting 32 from both sides of inequality

$=> 68-32 < \large\frac{9}{5} $$ C < 77 -32$

$=> 36 < \large\frac{9}{5} $$C<45$

Multiplying by positive number $\large\frac{5}{9}$ on both sides, of inequality

$=> 36 \times \large\frac{5}{9} < \frac{9}{5} \times \frac{5}{9} $$C < 45 \times \large\frac{5}{9}$

$=> 20 < C <25$

Step 3:

The required range of temperature in degree ceisius is between $20^{\circ}$ and $25^{\circ}C$