assuming you have o.4g of Y(OH)3, calculate the mass of Ba)2 required to produce YBa2Cu3O7.

Is that BaO2 for Ba)2? Is that really BaO2 or BaO. BaO2 is barium peroxide, not oxide.
Y(OH)3 ==> YBa2Cu3O7

Step 1. Convert 0.4g Y(OH)3 to mols Y(OH)3.

Step 2. Multiply by 2 to convert mols Y(OH)3 to mols BaO2 because the ratio of Y to Ba in the product is 1:2. There isn't enough information to write the full equation but this is the best guess we can make with the info provided. We are making the assumption that all of the Ba goes into the product and there are no other Ba products formed.

Step 3. Convert mols BaO2 to grams BaO2 by multiplying mols from step 2 by molar mass BaO2.

Post your work if you get stuck.