f (x) - - sq rt x+6 and g (x) = -4 sq rt x+3 describe the transformation

Please be careful with your typing [f(x)=-sqrt(x)+6 ... right? g(x)=-4*sqrt(x)-3 ... or -4*sqrt(x)+3 ... one or the other, right?

If so, you are dilating by a factor of 4, -1 versus -4 as multiplier of sqrt(x); and, translating up 3 units (6 versus 3) or 9 units (6 versus -3).