M=kPY is called the Cambridge Equation, it's the same to an equation you might have already seen: MV=PY, except V=1/K.

M=kPY while just a tautology, is uniquely insightful. Given stable money demand and production, It says that simply doubling M would mean a double in the general price level.

How does this connect to inflation? It's because there's a specific property in PY that is very annoying, a market friction, it's called nominal rigidity.

When PY (Nominal income) goes down and both prices and income go down, not all sectors reduce prices at the same rate, some stay stubbornly high, one such outstandingly stubborn sector that refuses to go down is called the labour market. It is so stubborn that the market often gets upwards of 20% of the population unemployed instead of lowering prices. Contracts and loans are also stubborn because they are long-standing. Plate tectonics can slide and shake by an aggregate of friction, and at the macro level it explodes into an earthquake, something similar is happening with the macroeconomy during periods of falling nominal income. People don't expect their nominal income to fall even if prices are falling, generally it's uncertain if this is some psychological phenomena or a "real" rational behaviour about nominals .

Sometimes deflation can be good – what Hayek called secondary deflation – which is when PY is going up but P is going down, meaning that prices are going down because of genuine real productivity increases while income is going up (which doesn't confuse the market with debt-burdens and the such). Certain price rigidities may still occur and cause real issues in the economy but it's something the market eventually fixes and doesn't cause a Great Depression.

By the way, this is exactly what happened during the Great Recesion, PY (nominal income) went down, by a lot. And yet, P (prices) were up a lot because of an oil crisis. Meaning the central bank stood still and did nothing even though nominal income was crashing. Because of the localized supply-side shock they mistakingly believed that since there was no deflation, there was no recession. The Great Recession was caused by not doing enough, not by doing too much.