Вы можете сделать что-то вроде этого.
div#thesishereyay {
margin-top: 50px;
margin-left: 120px;
position: absolute;
opacity: 0;
background-color: #000000;
}
h4.thesis {
margin: 10px;
}
li.thesisbutton {
position: absolute;
margin-top: 15px;
margin-left: 112px;
opacity: 1;
}
.nav:hover ~ #thesishereyay {
opacity: 1;
}
<div class="main">
<ul class="nav">
<li class="thesisbutton">Thesis</li>
</ul>
<div id="thesishereyay">
<h4 class="thesis">
Thirst for triumph during the<br>
Vietnam war in order to prevent<br>
a U.S. humiliation led to Lyndon<br>
Johnson lying to the American public<br>
about the Gulf of Tonkin incident to<br>
gain support for the Gulf of Tonkin<br>
resolution, which resulted in the<br>
continuation of the war and the<br>
tragedy of more lives being lost<br>
for a war being fought in fear of what<br>
might happen if the U.S. was defeated.</h4>
</div>
</div>