Break it down. We have
sum = expression
Sum is of type byte. What is the type of expression? Break it down. Expression is
summand1 + summand2
Summand1 is of type byte. What type is summand2? Break it down. It is:
test ? consequence : alternative
Test is of type bool. Alternative is of type byte. What type is consequence? Break it down! It is:
summand3 + summand4
That's byte + byte. Byte + byte is int, so consequence is of type int.
Now we have enough information to work out the type of summand2. Consequence is int, alternative is byte, and int is the more general of those two types. (Because every byte is convertible to int but not every int is convertible to byte.)
Therefore the type of summand2 is int. So we have sum equal to a byte plus an int. Byte plus int is int, and therefore we have int assigned to byte. Which is an explicit conversion, not an implicit conversion.