Question

what does the transformation $f(x) \mapsto f(x - 4) + 6$ do to the graph of $f(x)$?
translates it 6 units left and 4 units down
translates it 4 units right and 6 units down
translates it 6 units right and 4 units down
translates it 4 units right and 6 units up

Explanation:

Step1: Analyze horizontal shift

For $f(x-h)$, $h>0$ shifts right 4 units.
Transformation: $f(x) \to f(x-4)$

Step2: Analyze vertical shift

For $f(x)+k$, $k>0$ shifts up 6 units.
Transformation: $f(x-4) \to f(x-4)+6$

Answer:

translates it 4 units right and 6 units up