As you can see I have 2 G notes to play, one in the right hand melody and other in the left hand chord, how am I supposed to play this?
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You will play the G again in your RH as notated. In this instance, the pedal will sustain the LH G (see the pedal marks below the bass clef). Therefore, you’re good to lift your LH thumb from that G to allow the RH to play it.
Note that it is not usually recommended to rely solely on the pedal to sustain notes. Normally, even if there is a pedal marking (except in the case of staccato), you should keep the note depressed the full value. However, in this instance, you don’t really have a choice. You’ve got to allow that RH G to be played, especially since it seems to be the melody of the song!
I would definitely recommend keeping the other two LH notes depressed for their full value - the G in question, played by the LH thumb, should be the only one you need to release. Doing this will make it completely unnoticeable to the listener that you are “cheating” one note with the pedal (by necessity, of course).
Sometimes you see the hands overlap like this in old keyboards music. In those cases it can be understood the music would have been played on an instrument with two manuals. Harpsichords and organs often have two manuals.
In modern times people sometimes stack up two electronic keyboards. You could play overlapping hands that way too.
I suspect this is just an arrangement someone made on a computer without any concern for what a real human has to do with their hands on a real piano.
As the other answers say, on a piano with one keyboard you can just release the
G in the left hand and hit it again with the right hand for the second
G. You have no other choice and it cannot be play exactly as written on a single keyboard.