Question 345006
You have to expand all of the products and get one big equation. 
Then match the coefficients of the terms.
{{{ A(x+1)(x+3) + B(x-1)(x+4) + C(x+2)(x+3) = 6x^2 +34x + 46 }}}
{{{A(x^2+4x+3)+B(x^2+3x-4)+C(x^2+5x+6)=6x^2+34x+46}}}
{{{(A+B+C)x^2+(4A+3B+5C)x+(3A-4B+6C)=6x^2+34x+46}}}
So now you have three equations with three unknowns.
{{{A+B+C=6}}}
{{{4A+3B+5C=34}}}
{{{3A-4B+6C=46}}}
Solve for A,B,C using substitution, elimination, or matrix methods.
Re-post if you need more help.