changean event is not raised for an element div. You will have to attach it to the switches, for which they will obviously be called.
It is also recommended to avoid inline event handlers and attach handlers in JS to avoid pollution HTML
HTML
<div id="radiobuttons" class="container" name="buttons" align=center>
<h2>I Want my Building to be Made of:</h2>
<ul>
<li>
<input type="radio" id="brick-option" name="material" value="1">
<label for="brick-option">Bricks</label>
<div class="check"></div>
</li>
<li>
<input type="radio" id="wood-option" name="material" value="3">
<label for="wood-option">Wood</label>
<div class="check">
<div class="inside"></div>
</div>
</li>
<li>
<input type="radio" id="stone-option" name="material" value="2">
<label for="stone-option">Stone</label>
<div class="check">
<div class="inside"></div>
</div>
</li>
</ul>
</div>
<p id="paragraph" align="center">0</p>
Js
var radioButtons = document.querySelectorAll('input[type=radio]');
for (var i = 0; i < radioButtons.length; i++) {
radioButtons[i].addEventListener('change', function() {
if (this.checked) {
document.getElementById("paragraph").innerHTML = this.value;
}
});
}
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