If there is a 0.3% chance of something happening one day, what is the possibility of it happening throughout twenty days?

Try by multiplying 0.3x20

You mean of it happening within 20 days?

Well if there is a 3/10 probability of it happening in any given day, there is a 7/10 probability of it not happening on any given day. The probability of it not happening at all in 20 consecutive days is:

(7/10) ^20

So the probability of it happening at least once in 20 days is:

1 - (7/10) ^20≈9992/10000 (about 99.92%)