1. **State the problem:** We have the function $f(x) = x^4$ and want to find the formula for $g(x)$, which is the graph of $f(x)$ shifted left by 6 units. 2. **Recall the rule for horizontal shifts:** Shifting a function $f(x)$ left by $h$ units results in $g(x) = f(x + h)$. 3. **Apply the rule:** Since the shift is left by 6 units, $h = 6$, so $$g(x) = f(x + 6)$$ 4. **Substitute $f(x)$:** Given $f(x) = x^4$, substitute $x + 6$ for $x$: $$g(x) = (x + 6)^4$$ 5. **Final answer:** The formula for $g(x)$ is $$g(x) = (x + 6)^4$$ This means the graph of $f(x)$ is shifted left by 6 units to get $g(x)$, preserving the shape but moving the curve horizontally.