How many g of MgCO3 (s) are needed to make 1.2 L of 1.5 M MgCl2 (aq) solution?

Molar mass of MgCO3 is 84.313 g/mol

You can calculate this from data on the periodic table:

Molar mass Mg = 24.305g/mol

molar mass C = 12.011g/mol

molar mass O = 15.999g/mol mass 3 mol = 47.997g

Total = 84.313g/mol

Mass to be used in 1.2L of 1.5M solution = 84.313g * 1.2L * 1.5mol / L = 151.763g

I have not taken significant figures into account

The balanced equation you provide is not necessary in this calculation