Final answer:
Barney must recognize zero dollars of income for painting his own house, as the realization requirement requires a transaction and actual accession to wealth, which did not occur in this self-service activity.
Step-by-step explanation:
According to the realization requirement in tax law, Barney must recognize zero dollars of income for painting his own house. The realization requirement stipulates that income is recognized when an economic transaction occurs and there is a clear accession to wealth over which the taxpayer has complete dominion.
Since Barney did not engage in a transaction with another party and merely saved money by painting his own house, there was no realization of income according to the tax law principles. According to the realization requirement, Barney must recognize the amount of income that he saved from painting his house. In this case, he saved $3,000, so this amount should be recognized as income for Barney.