There is not a hard and fast rule for how big your emergency fund should be but there are definitely a lot of folks in the personal finance community who have at least 6 months in some type of readily available account that's not tied up in 401k or other investment funds which have early withdrawal penalties.

How much you save comes down to the individuals ability to do so and how much risk they are at if they were to suddenly lose a source of steady income and how much debt they currently have. For people with a lot of ongoing expenses, it'd be smart to try and pad up some safety net so they don't have their life completely fall apart if they somehow lost their job. This also might vary if you are single income or multiple streams for the household.

6 months is probably on the higher side since there's the opportunity cost of not investing surplus money somewhere that could have a higher rate of returns. Usually money that is in emergency funds have lower interest rates as a tradeoff. And if you have upwards of 4 months or more, you can use that time to draw from other accounts for more money if you see that the emergency fund isn't enough.