This answer doesn't require that you know the what type of display (inline, etc.) the hideable element is supposed to be when being shown:
.hoverable:not(:hover) + .show-on-hover {
display: none;
}
<a class="hoverable">Hover over me!</a>
<div class="show-on-hover">I'm a block element.</div>
<hr />
<a class="hoverable">Hover over me also!</a>
<span class="show-on-hover">I'm an inline element.</span>
This uses the adjacent sibling selector and the not selector.