i am struggling to understand this.

High nominal interest rate rises the real interest rate, so the opportunity cost of holding the money becomes greater, so people would spend or invest the money, the velocity of money increase and mv=py so less money suppy mean less siegnorage,

when there is high infaltion, the real interest rate decreases, so the opportunity cost of holding the money becomes smaller, so people keeps the money in hand so decline in money supply and less seignroage ?? but now the borrowing cost would decrease so people would invest and increase in demand for money so more seignorage? i am confused which is which?

Seigniorage is the difference in face value of money, such as a $0.25 quarter coin, and the cost to produce it. Seigniorage may be counted as positive revenue for a government when the money it creates is worth more than it costs to produce. It can also be termed as a source of revenue for governments as the value of money printed is generally higher than the cost of producing it. As obvious, if the currency produced values more than the cost involved in its production, the government earns a profit. If the cost involved in its production crosses its value, then the government suffers a loss.

Inflation tax is the loss that is sustained by the holder of real money balances and non-indexed government bonds due to inflation.

Step-by-step explanation

Seigniorage is the difference in face value of money, such as a $0.25 quarter coin, and the cost to produce it. Seigniorage may be counted as positive revenue for a government when the money it creates is worth more than it costs to produce. It can also be termed as a source of revenue for governments as the value of money printed is generally higher than the cost of producing it. As obvious, if the currency produced values more than the cost involved in its production, the government earns a profit. If the cost involved in its production crosses its value, then the government suffers a loss.

Inflation tax is the loss that is sustained by the holder of real money balances and non-indexed government bonds due to inflation.

Seigniorage causes inflation. when there is high inflation, the real interest rate decreases, so the opportunity cost of holding the money becomes smaller, so people keeps the money in hand so decline in money supply and less seignroage this statement is correct because high inflation leads to unemployment therefore people lack money and this causes less seigniorage. When real money balances are constant over time, that is M/P=M-1/P-1, seigniorage and inflation tax are equal. 

But now the borrowing cost would decrease so people would invest and increase in demand for money so more seignorage. The seignorage will decrease because there will be a lot of money in the economy to help generate enough revenue.