Mannose-6-phosphate is a post-translational modification found on proteins important to the functionality of the lysosome (such as acid hydrolases). Ubiquination is a signal for proteins to be brought to the proteosome and degraded. Myristoylation involves the addition of a fatty acid chain, and is often seen in proteins targeted to the plasma membrane. Acetylation is a common modification found on histones that can help make genes transcriptionally active. 

An isomerase is an enzyme that catalyzes the rearrangement of bonds in a single molecule. For example glucose-6-phosphate isomerase catalyzes the conversion of glucose-6-phosphate into fructose-6-phosphate during glycolysis.

A hydrolase catalyzes a hydrolytic cleavage reaction, a kinase catalyzes the addition of a phosphate group, and a polymerase catalyzes polymerization reactions.

The correct answer is ubiquitination. Ubiquitin is added to the substrate protein to target the protein for degradation by the proteasome, serving as an efficient mechansim to control cellular protein levels. Myristoylation, palmitoylation, isoprenylation, and glycosylation are all post-translational protein modifications that involve the addition of a 14-carbon saturated acid, a 16-carbon saturated acid, an isoprenoid group, and a glycosyl group, respectively. These modifications have diverse functions, however, do not initiate the degradation of the protein.  

While each of these molecules could potentially be bound to a protein as a post-translational modification, the only one listed that is a fatty acid is palmitate. Thus, this is the correct answer. 

The correct answer is adenosine triphosphate (ATP). In order to phosphorylate a substrate, kinases catalyze the hydrolysis of ATP to adenosine diphosphate (ADP) and inorganic phosphate. This released phosphate by the hydrolysis reaction is covalently added to an amino acid residue on the substrate. Nicotinamide adenine dinucleotide phosphate, flavin adenine dinucleotide, and nicotinamide adenine dinucleotide are proton carriers. Guanine nucleotide exchange factor aids in exchanging guanine diphosphate for guanine triphosphate in a substrate. 

The correct answer is all of the answers are cellular processes in which ubiquitination is involved. Post-translational ubiquitination of proteins initiates many cellular processes by altering protein activity and the proteins that interact with the ubiquitinated protein. 

A kinase is an enzyme that adds a phosphate group. Do not get this confused with a phosphatase. A phosphatase is an enzyme that removes a phosphate group. The other enzymes listed do not deal with the addition or removal of a phosphate group from a protein.

All of the given answers are ways that a cell may regulate protein concentrations. Polyubiquination is a signal for the protein to be degraded by a proteasome. Gene silencing will prevent transcription, which will lower the amount of mRNA template that can be translated into a protein. RNAi will degrade specific mRNAs or prevent the translation of specific mRNAs into proteins.

Polyubiquination is a modification results from the binding of small ubiquitin residues to a protein. Polyubiquination of a protein signals damage or problems with functionality, and triggers the mechanisms that result in protein degradation. The polyubiquinated protein is then brought to a proteasome (a complex of proteins) that will degrade the protein.

Glycosylation involves the attachment of a carbohydrate complex to a protein. The identity of the carbohydrate is essential for determining the functional outcome of glycosylation, but generally results in signaling and transport labels for the protein. Glycosylation is not by itself a signal to be brought to either a proteasome or a lysosome.

E1, E2, and E3 all have unique activities that progress step-wise to activate ubiquitin and then attach those ubiquitins to mark a protein for degradation. Their functions are not redundant, nor do they activate acids, autophagosomes or ATP complexes over the course of their pathways.