Me on this question

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Recall that
f(x)->f(x-h)  shift right h units
f(x)->-f(x)    reflect over x-axis
f(x)-> f(-x)   reflect over y-axis
f(x)-> 2f(x)  vertically stretch by 2 units
and
f(x)=x
g(x) has a slope of -2, and a y-intercept of 6, so
g(x)=-2x+6

A. 
f(x)->f(x+2) -> f(-x+2) -> 6f(-x+2) =6(-x+2)=-6x+12  [ does not equal g(x) ]

B. 
f(x)->-f(x) -> -2f(x) -> -2f(x)+6 = -2x+6    [ equals g(x), so YES ]

C.
f(x)->f(x-3)->f(-x-3)-> 2f(-x-3) = 2(-x-3)=-2x-6     [ does not equal g(x) ]

D. 
f(x)->f(-x)->2f(-x)->2f(-x)+6=-2x+6            [ equals g(x), so YES ]

E. 
f(x)->f(x+3)->f(-x+3)->2f(-x+3)=-2x+6       [ equals g(x), so YES ]

F.
f(x)->f(x)+6->-f(x)-6->-2f(x)-12 = -2x-12    [ does not equal g(x) ]

Following images show the sequence of transformations for cases A through E, of which cases B,D and E result in the given graph.

Sorry, I am only allowed 5 images, so F will not be illustrated.

B. 16is the absolute value