This is a farily simple task it might be a duplicate and the solution is found easily on the internet ,but please read through my answer and let me know if you need further instructions.
Using javascript events and functions:
<li>
<div class="wicoaching">
<a href="index.php" style="border-top:0px" onclick="ChangeImage();">
What is Coaching?</a>
</div>
</li>
This means that whenever someone clicks on 'What is coaching?' a function called ChangeImage will be executed.
Now you need to declare the function.
<script>
function ChangeImage{
var thePic = document.getElementById('MyImage');
// Note you need to add a name or image to your img tag.
thePic.src = "SomeOtherImage.gif";
}
</script>
If you instead want to remove the image and add another one:
var imageToBeRemoved = document.getElementById('MyImage');
var Parent = imageToBeRemoved.parentNode;
Parent.removeChild(imageToBeRemoved);
Now it's gone from your DOM. It would go inside your ChangeImage function, instead of changing the image source.
If you want to add another one with a different Source :
var newImage = document.createElement("img");
NewImage.src = 'MyNewImage.jpg';
Parent.appendChild("newImage"); // alternatively, you can reference to parent by its ID or Name using getElementById or a similar method.