P(H|G) = 0.6 means that  the ratio  P(H ∩ G) / P(G) = 0.6  (by the definition of conditional probability).


Substitute here the given data, and you will get

    P(H ∩ G) / 0.5 = 0.6.


It implies  P(H ∩ G) = 0.5*0.6 = 0.3.



Finally, use the general probability formula for the union

    P(H OR G) = P(H) + P(G) - P(H ∩ G),

which is valid for any events H and G.


Substitute all given and found values into this formula, and you will get

    P(H OR G) = 0.3 + 0.5 - 0.3 = 0.5.