To shift a graph right N units, we replace x by x-N in the equation.
To shift a graph left N units, we replace x by x+N in the equation.
To shift a graph up N units, we add +N to the entire rights side of 
the equation.
To shift a graph down N units, we subtract N from the entire right 
side of the equation.

We start with the graph of y = |x|  The red graph below:



Then we shift it right 1 unit by replacing x by x-1

y = |x-1|    The green graph below:



Then we shift it down 4 units by subtracting 4 from the whole right side.

y = |x-1|-4      The blue graph below:



Edwin

Guided by general rules of transforming functions and graphs,

the sequence of parallel translations from y = |x| to z = |x-1| - 4  is


    (a)  parallel horizontal translation 1 unit right  

and

    (b)  parallel vertical translation 4 units down.