How many grams of licl are needed to make a saturated solution with 300. g of water at 20°c?

You need the solubility of the LiCl in water at 20°C.

The solubilities are shown in tables. Many books contain those tables. You have to make sure that the solubility is shown in the same solvent and at the same temperature that you are going to prepare the solution.

In this case the solubility of LiCl in water at 20°C is 83.05 g of LiCl in 100 g of H2O. Check if your book and your teacher work with the same value.

Using 8.05 g LiCl / 100 g of water you get:

300 g of water * 83.05 g LiCl / 100 g of water = 249.15 g of LiCl.

Answer: 249.15 g of LiCl