1
general::
Phrase(s): think something through
to run over and try to settle something in one’s mind. • Let me think this through and call you in the morning. • I will think through this matter and get back to you.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
Also, think out. Arrive at a thorough understanding of; devise or contrive thoroughly. For example, That answer doesn't work; I don't believe you've thought the problem through, or He thought out a far more efficient method. The first term dates from the early 1900s, the variant from the mid-1800s. Also see THINK UP.
American Heritage Idioms