1. You have to overexpress and Knock-down/Knock-Out your transcription factor in your Primary Y cells/Y Cell-line and check the Protein levels of X by simple Western Blot.
2. To verify the transcription of Gene of Protein X, You can try qPCR of your desired target gene, in your desired cell-lines(with or without Knock-down/Knock-out of transcription factor)