My answers are -33g of butane and -99 g of CO2. I'm looking at other answers and their numbers are positive. Why?

I've calculated the amounts and got positive numbers, but otherwise the same values that you arrived at:

-1500 kJ/-2658 kJ/mol of butane = 0.56 moles butane

(0.56 mol butane)(58.5 g/mol) = 33 grams butane

(0.56 mol butane)(4 moles CO2/1 mol butane)(44 grams/mol) = 99 grams CO2

Your error was most likely in not labeling the 1500 J of heat liberated as negative. The `Delta` H per mole of reaction is given as a negative value,...

I've calculated the amounts and got positive numbers, but otherwise the same values that you arrived at:

-1500 kJ/-2658 kJ/mol of butane = 0.56 moles butane

(0.56 mol butane)(58.5 g/mol) = 33 grams butane

(0.56 mol butane)(4 moles CO2/1 mol butane)(44 grams/mol) = 99 grams CO2

Your error was most likely in not labeling the 1500 J of heat liberated as negative. The `Delta` H per mole of reaction is given as a negative value, -2658 kJ, because the reaction is exothermic. Similarly, the heat evolved for an amount of butane other than one mole will have a negative value. The negative signs cancel out in the first step when -1500 is divided by -2658. 

An exothermic reaction has a negative  `Delta` H and an endothermic reaction has a positive  `Delta` H because the  `Delta` H describes the energy change of the substances reacting. When heat is released, the surroundings gain heat and warm up. That heat came from the reaction, and was released because the products have less chemical potential energy than the reactants. Since energy was lost by the reacting substances the  `Delta` H is negative.