====================================================
$\small (6a-4b)(a+2b)-(2a-b)(5a+3b)+a(4a-7b)+6b^2 =$
$\small = 6a^2+12ab-4ab-8b^2-(10a^2+6ab-5ab-3b^2)+4a^2-7ab+6b^2 =$
$\small = 6a^2+8ab-8b^2-(10a^2+ab-3b^2)+4a^2-7ab+6b^2 =$
$\small = 6a^2+8ab-8b^2-10a^2-ab+3b^2+4a^2-7ab+6b^2 =$
$\small = (6-10+4)a^2+(8-1-7)ab+(-8+3+6)b^2 =$
$\small = \cancel{0a^2}+\cancel{0ab}+b^2 =$
$\small = b^2 $