Mineral oil is a non-polar hydrocarbon. Water is a polar solvent, and tetrahydrofuran is a polar aprotic solvent. Polar solvents are solvents that have a net electrical charge, while non-polar solvents do not. Non-polar solvents are immiscible with polar solvents, meaning that they do not mix together.
Therefore, mineral oil is not soluble in a solution of water and tetrahydrofuran.