The best search would be the first one.
Commissioning adj3 mental health service$ - this search would bring up references where commissioning is within 3 words of mental health services. It keeps it relevant but not too narrow.
Commissioning mental health service$ - this search would look for occurrences of the words: commissioning, mental, health and services, but not particularly related to each other. In other words this search would be too broad.
"commissioning mental health service$" - this would be a good search to perform in addition to the first one, as would search for this exact phrase. So, the results would be very relevant, but it would nevertheless be too restricted and not bring up references where the words are in close proximity to each other.
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