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.

249.15 g of LiCl  

Mass is the amount of matter in an object.  weight is the measurement of the pull of gravity on an object.  say for example, you travel to the moon which has a different gravitational field compared to the gravitational field of earth. (gravitational fields: earth = 1, moon = 0.165)  now when you are on the moon, the pull of gravity on you is different than on the earth. and as weight is the measurement of the pull of gravity on an object, that means yes, your weight can and will change on the moon.  however, on the moon, on earth or even on jupiter, the amount of mass inside of you remains the same. meaning your physical mass remains constant.  in conclusion it is possible for your weight to change as your mass remains constant.