Bromine (br2) is produced by reacting sea water with chlorine (cl2) by the following reaction. what mass of cl2 (in kg) is needed to produce 1.0 kg of br2?

Haha ironically I had this problem not too long ago, I hope by this we will both be better students. Everyone just needs practice. Ok stop to pep talk and lets go. I'll try to go step by step. 

So basically since this is a balanced equation, the ratios of mols of the elements are equal, atom wise. 

So you notice they give you Br2 is 1.0 kg (1000g) and that means there are 2 mols of Br2. And its asking for Cl2, (on the left) it also has 2 mols. 
Then you can start from 1000g Br2 and multiply with 2 mol Br2 and 159.8g Br2 on the bottom. The 159 8 is the actual grams per mol. Then when you write this down, continue multipying with the next fraction. 

Since you know the molar mass of Cl2 is 70.4 and you know theres 2 mols, you can say that 2 mols of Br2 = 2 mols of Cl2 so you should be able to multiple 2 mol Br2 / 159.8g Br2 with 70.4 g Cl2 / 2 mol Cl2. Bam the mols cancel out and you have the grams for Cl2. Multiple all that out and you should get 443g Cl2. Notice how the beginning question gives 2 significant figures, so technically 440g Cl2 is more of an exact number.