How to make taxonomy term checkbox display multicolumn?
You can accomplish this using CSS, specifically flexbox. The exact element you need to target with your CSS rules will depend on your theme. You will need to add the following CSS to the element that contains your checkbox items. 

.container {
  display:flex;
  flex-direction: column;
  flex-wrap: wrap;
  height:20vh; /* You will need to set a height on the container
                  to get the look you want, this is an example height */
} 


In my example, I'm using Drupal 8 and the Seven administration theme. On an add/edit node page, I have a taxonomy field (the default tags) using  checkboxes. You can see in the below image that each checkbox element is wrapped in a div and all of those divs are wrapped in a container div with the id edit-field-tags. So, if I apply the above CSS to that container, I get the results that match your goal:



You may want to play around with the alignment or spacing of the flex elements, for more information on that that I recommend checking out "A Complete Guide to Flexbox" on CSS Tricks.