A student pours 36.4g of water at 11 C into a beaker containing 123.0g of water at 11 C. The density of water at 11 C is 1.00g/mL. They want to...

The mass of final solution would simply be the two masses added together. In this case, it would be 36.4g + 123.0g = 159.4g

Since the temperature of both initial water samples are at 11C, the final temperature of the mixed water will also be 11C, assuming the environment is also at the same temperature so that the water hasn't heated up or cooled down due to heat transfer between the beakers and the environment.

Since the water temperature does not change, the final density of the mixed water will also remain at 1.00g/ml. If there was a problem where the temperature of the water was changed, you would have to determine what the density of water is at the new temperature. Alternatively, you may be given the final volume of water in the mixed sample and be asked to calculate density based on that. In that case, the density would be mass divided by volume, or 159.4g divided by X volume.