For f(x) = x2 and g(x) = (x − 4)2, in which direction and by how many units should f(x) be shifted to obtain g(x)? left 4 units up 4 units right 4 units down 4 units

Short answer 4 units to the right.

Remark
Graph the two equations.
The purple graph is y = x^2
The black graph is y = (x - 4)^2

Rule
1. When a constant is inside the brackets, the graph moves left or right. To tell which use the second part of the rule.
2. use y = (x + a)^2 as your example.
if a > 0 the graph moves left.
if a < 0 then graph moves right.
Just the opposite of what you would expect.