Answer:The correct answer option is C. [tex] g ( x ) = | x - 4 | + 6 [/tex].Step-by-step explanation:We know that the transformation which shifts a function along the horizontal x axis is given by [tex]f(x+a)[/tex], while its [tex]f(x-a)[/tex] which shifts the function to the right side.Here we are to shift the function 4 units to the right and 6 units up.Therefore, the function will be:[tex] g ( x ) = | x - 4 | + 6 [/tex]