Tableau Zen Master Ken Flerlage created a great blog post and accompanying template for building sunburst charts in Tableau. It's a little complicated but certainly possible.
One thing I really should have mentioned in the post because it's the most important thing. The sunburst chart is interactive and will create new sunburst charts. For example if you click medicine (on the upper middle connected to biology) it will create a new sunburst chart with medicine as the center and then secondary and tertiary categories associated with just medicine.
It's all based on the hierarchy of information. You would need to build out your dataset in a hierarchy so each item is at a certain level. For example, Explore would be the top level - in a field you could call Level 1. The second column/field would be Level 2 and would consist of Biology, Chemistry, Engineering, etc. You would keep adding Levels until all of the hierarchy information is in your dataset.
You could then build the initial view with Explore in the middle. You'd need a filter in place to only show the highest level and two below it. I think you could use a Window_Max calculation to figure out the highest level in the view. Initially it would be level 1, but after you click something,you'd want the new level to become the highest level and it would show 2 below that - so if you click Cell Biology, your highest level would now be level 3 so you'd show levels 3 through 5.
You would need some type of worksheet or dashboard action where the worksheet filters itself based on the level you click - target and source sheet would be the same, and you'd have the level field = the top level field (which is used for your filter) and maybe something like the category you click becomes the top category and all other categories at that level are filtered out.
Obviously this is pretty complicated. The best way to handle things like this in Tableau is to start building the initial viz - which would be the initial sunburst chart, and then start to add filtering to it after that.
Also in 2018.3, you may be able to do this with set actions