When serving as preposition, tōngguò通过means ‘by’ or ‘through’ while jīngguò经过 means ‘after’.
tōngguò通过 matches with the medium includes people, activities and things while jīngguò经过 matches with the process. For example,
Tōngguò zhège huódòng，wǒ xuéxíle hěnduō dōngxī
Through this activity I learned many things
‘I learned a lot through this activity.’
Jīngguò rènzhēn sīkǎo， tā cízhíle
After carefully consider he resign
‘He resigned after the careful consideration.’