graph

We have a "zero"   at x  = 4

This means that , in the numerator,   4  + A    =   0

So A =  -4

Also....we have a horizontal asymptote  at   y =  -1

Looking at the  coefficients on the  x variables in the numerator and denominato, taking their ratio  and setting it equal to this asymptote, we have that

1 / B =  -1

So   B   = -1

And we have a vertical asymprore at  x  = 3

This means  that, in the denominator,  -1 (3)  + C  = 0  →   C = 3

A + B + C =   

-4 -  1  +  3   =

-2

See the graph here to  confirm this  : https://www.desmos.com/calculator/tx6zbax7ra