If you know that one of the two columns is always going to be taller than the other, then you can do something like this:
Just give position: absolute to the shorter column and make it stretch from top: 0 to bottom: 0.
HTML:
<div class='container'>
    <div class="containerLeft">
        <h2>1.</h2>
        <p>First, let's play a video.</p>
    </div>
    <div class="containerRight">
        <img src="http://tctechcrunch2011.files.wordpress.com/2012/09/michael-headshot-red.jpg?w=288" />
    </div>
</div>
CSS:
.container { position: relative; }
.containerLeft { /* shorter column */
    position: absolute;
    top: 0; bottom: 0; left: 0;
    width: 38%;
    padding: 2%;
    background-color: crimson;
}
.containerRight { /* taller column */
    margin: 0 0 0 42%;
    width: 58%;
    background: dodgerblue;
}
If you don't know for sure which one of them is going to be taller, then you can simulate the fact that they are of equal height by using a background gradient on their parent.
HTML is the same, CSS becomes:
.container {
    overflow: hidden;
    background: -webkit-linear-gradient(left, crimson 42%, dodgerblue 42%);
    background: -moz-linear-gradient(left, crimson 42%, dodgerblue 42%);
    background: -o-linear-gradient(left, crimson 42%, dodgerblue 42%);
    background: linear-gradient(left, crimson 42%, dodgerblue 42%);
}
.containerLeft, .containerRight { float: left; }
.containerLeft {
    width:38%;
    padding: 2%;
}
.containerRight { width: 58%; }
However, CSS gradients don't work in IE9 and older, so if you want a solution for IE8+, then you can try this
which uses :before and :after pseudo-elements.
.container {
    overflow: hidden;
    position: relative;
}
.container:before,.container:after {
    position: absolute;
    z-index: -1;
    top: 0; bottom: 0;
    content: '';
}
.container:before {
    left: 0;
    width: 42%;
    background: crimson;
}
.container:after {
    right: 0;
    width: 58%;
    background: dodgerblue;
}
.containerLeft, .containerRight { float: left; }
.containerLeft {
    z-index: 2;
    width:38%;
    padding: 2%;
}
.containerRight { width: 58%; }