When a variable is being multiplied and it's negative such as in (-4k = 12), you simply perform the inverse operation (in your case division) and keep the sign the same.
e.g.
-4k = 12
-4k ÷ -4 = 12 ÷ -4
k = -3
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It is a coefficient.
constant
it's only negative if it's being multiplied by a positive number. If it's being multiplied by another negative number than it will be positive.
That would be negative three. A negative multiplied by a negative is a positive. A negative multiplied by a positive is still a negative.
Negative 4 multiplied by 3 is equal to negative 12.