To find the vertical asymptote, take the denominator and set it equal to zero. So x + 4 = 0 -> x = -4.
(Note that asymptotes are not numbers, but equations of lines. So to say that a vertical asymptote is -4 is not correct; you need to write x = -4.)
To find the horizontal asymptote, first, note the degrees of the polynomials in the numerator (I'll denote ) and denominator ( ).
If , then the horizontal asymptote is y = 0.
If , then there is no horizontal asymptote. (There is a slant asymptote.)
If , then the horizontal asymptote is y = the ratio of the leading coefficients of the polynomials.
In your problem, the degrees of the polynomials are the same (1). The leading coefficient of the polynomial in the numerator is -1, and the leading coefficient of the polynomial in the denominator is 1. So the horizontal asymptote is y = -1/1 = -1.