Answer
B∪C = {b,c,d,e,f,g,h}
Work Step by Step
U = {a,b,c,d,e,f,g,h}
B = {b,g,h}
C = {b,c,d,e,f}
B∪C shows all the elements of set B and set C and excluding repeated ones.
List the elements from the first set, namely b,g,h. Now add to the list the elements in the second set that are not in the first set. This includes element in the second set, namely c,d,e,f.
The elements of B∪C are b,c,d,e,f,g,h.
Therefore B∪C = {b,c,d,e,f,g,h}