Hey there!
A half-life means after a certain amount of time, half of that substance will be gone/changed after that time.
There are 3 half lives in 11.46 days because 11.46 ÷ 3.82 = 3.
So, we divide the 3mg sample in half 3 times.
3 ÷ 2 = 1.5
1.5 ÷ 2 = 0.75
0.75 ÷ 2 = 0.375
There will be 0.375mg of radon-222 remaining after 11.46 days.
Hope this helps!