Intuition behind Real Money Demand and Real Money Supply
They're in monetary units! Let's say an economy has a money supply of $100$ $mu$ and a price level of $1$. Another economy has the same money supply but a price level of $1.5$. Which economy has the bigger real money supply? The first, obviously. In the first hypothetical economy, you can think of the average transaction as one involving smaller amounts of currency. Real money demand will of course depend on nominal income $Y$. An increase in nominal income makes people demand more money because there's more transactions to be made.