The original function given is $f(x) = |x|$.

Now, we are asked to shift this function:

1. Left by 6 units: Shifting a function left by 6 units modifies the argument of the function. For a shift left, we add 6 to $x$. So the new function becomes $|x + 6|$.
2. Down by 7 units: Shifting a function down by 7 units means subtracting 7 from the function value. So we subtract 7 from the expression.

Thus, the new equation for the function $g(x)$ after shifting becomes: $g(x) = |x + 6| - 7$

Would you like a detailed breakdown of how shifts in functions work?

Here are 5 related questions:

1. How do horizontal and vertical shifts affect the graph of a function?
2. What happens to the graph of $f(x) = |x|$ if it is shifted right instead of left?
3. How can you determine shifts based on the equation of a function alone?
4. What would the graph look like if you shifted the function up instead of down?
5. How do reflections (flipping) relate to translations in functions?

Tip: Horizontal shifts affect the $x$-variable inside the function (e.g., $x + c$ for left), while vertical shifts affect the entire function by adding or subtracting a constant.