This job names the organelle that is the major site of ATP synthesis and three organelles involved in protein synthesis or modification or both

The main organelles responsible for ATP synthesis are the mitochondria. (http://micro.magnet.fsu.edu/cells/mitochondria/mitochondria.html)

Protein synthesis is accomplished by several organelles working together. First of all, the ribosomes are the site where the information is read off of the mRNA to create the protein. These ribosomes can be free or attached to the Rough Endoplasmic Reticulum. Once the protein is produced, it is process by the Golgi Apparatus and, if it is intended to be released from the cell, packaged into vesicles. (For more information, see http://web.mit.edu/esgbio/www/cb/organelles.html)

Both lysosomes and peroxisomes contain enzymes. Lysosomes are like the "stomachs" of the cell, in that they generally contain a mixture of digestive (hydrolytic) enzymes. These enzymes are used to digest materials taken into the cell by endocytosis or to degrade old, worn-out organelles. Peroxisomes contain oxidative enzymes and are used to break down materials produced during cell metabolism which would be toxic to the cell if allowed to accumulate, like hydrogen peroxide. (For more information, see http://cellbio.utmb.edu/cellbio/lysosome.htm)