You need to use the CONVERT_TZ function , but you did not specify which time zone you want to convert datetime to:
CONVERT_TZ(STR_TO_DATE(LEFT('06/01/2010 15:00:00 08:00', 20), '%m/%e/%Y %H:%i:%s'),
CONCAT('+', RIGHT('06/01/2010 15:00:00 08:00', 6)),
?)
You need to replace ?with the relevant time zone information.
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