Reduce using Boolean Algebra
Sometimes the best thing to do is to look at the truth table for the expression you are given.

\$(\bar BC + B)\$ gives this truth table.



Now, I am quite confident that you can see from this table why the \$\bar B\$ can be removed. Just think about it.

Alternatively, if you expand the original equation (otherwise know as applying Distributive Law), you get \$(\bar B+B).(C+B)\$, geddit yet?