When you're working with mixed numbers, you always want to make sure your fractions play nicely together. A fraction is just a proportion, meaning it can be scaled up or scaled down. To scale 5/6 and 4/15 so they'll be easily compatible with each other, you need to find a common denominator.
The smallest number that your existing denominators (the digits under/to the right of the slash) of 6 and 15 will both go into is 30. (6*5=30 and 15*2=30.) Keep your numerators (the digits over/to the left of the slash) in proportion by multiplying them by those factors as well, using equations that look like this:
(5/6)*(5/5)=25/30. So, your original value of 1 5/6 is equivalent to 1 25/30.
1 25/30 + 3 8/30 = 4 33/30.