The normal reading of this language is that if you know you are going to have to be away for 6 hours during the time you have the child that you must offer her the chance to keep the child. If you are on call then you don't know you are going to leave but if you get called and its going to be 6 hours then you need to give her the chance to watch the child.
Every situation is different and you should consult your own attorney to go over all the particular facts in your case. The answer given is only intended to provide general guidance regarding rights and responsibilities.
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