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The whole point is to think about which cells would be most prone to exogenous  mutations, and those are the cells that will be likely to utilize nucleotide excision repair. In this case, skin cells are consistently exposed to the external environment, which is why they are extremely PRONE to mutation. The biggest source of these mutations is UV light, which often causes thymine dimers and the inability to replicate DNA. On the other hand, capillary cells are not subject to any mutation-like forces (e.g. UV), which is why they don’t have as much use for nucleotide excision repair (though it is definitely used). Similarly, neurons are also not likely to be subject to an abnormally high mutation rate, which is why it is not a likely answer. And lastly, both platelets and RBCs don’t even have nuclei, which means they don’t have the normal 46 chromosomes; for this reason, they have very little proofreading activity and little (if any) nucleotide excision repair.