We are starting with the parent function f(x)=|x|

STEP 1: Vertically stretch the graph by a factor of 2, to get y=2|x|

STEP 2: Reflect the graph across x-axis, to get y=-2|x|

STEP 3: Shift the graph by 1 unit to the right, to get y=-2|x-1|

STEP 4: Shift the graph by 4 units downwards, to get y=-2|x-1|-4, which is the required function g(x)

STEP 1: Vertically stretch the graph by a factor of 2, to get y=2|x|

STEP 2: Reflect the graph across x-axis, to get y=-2|x|

STEP 3: Shift the graph by 1 unit to the right, to get y=-2|x-1|

STEP 4: Shift the graph by 4 units downwards, to get y=-2|x-1|-4, which is the required function g(x)