Answer
error: removing the second parentheses.
answer= $x^{2}+4x+9$
Work Step by Step
In the first step, the error is in removing the second parentheses.
It should be
$(4x^{2}-x+3)-(3x^{2}-5x-6)\\
=4x^{2}-x+3-3x^{2} \color{red}{ +5x+6}=$
...gather like terms.
$=4x^{2}-3x^{2}\quad-x+5x\quad+3+6$
$=x^{2}+4x+9$
