Density of unknown solution?
What you did in your explanation is correct. First find the difference in the weight:
$$20.3102-20.2367=0.0735 \ \mathrm{g}$$

We know that from your density of water:
$\mathrm{\frac{1\ g}{1\ mL}\ \text{that }\ 0.0735 \ g = 0.0735\ mL}$

Then the difference between the unknown and the vessel is calculated as:
$$20.300-20.2367 = 0.0933\ \mathrm{g}$$

and then density is expressed as mass over volume, so:
$$\mathrm{\frac{0.0933\ g}{0.0735\ mL}=1.2693_8\ g\ mL^{-1}}$$