Step 1 :The y-intercept of a function is the point where the graph of the function intersects the y-axis. This occurs when x = 0.
Step 2 :To find the y-intercept of the function \(f(x)=\log _{3}(x+4)+2\), we substitute x = 0 into the function and solve for y.
Step 3 :Substituting x = 0, we get \(f(0)=\log _{3}(0+4)+2\).
Step 4 :Solving this, we get the y-intercept as approximately 3.26.
Step 5 :None of the given options results in the correct y-intercept. The correct y-intercept for the function \(f(x)=\log _{3}(x+4)+2\) when x = 0 is approximately 3.26.
Step 6 :\(\boxed{3.26}\) is the final answer.