Hover your mouse over the border between the two spaces till you see a little double sided arrow....click hold and drag.
This standard for just about every user interface in existence. Same as windows explorer.
I highly suggest watching an introductory tutorial for after effects. Interface is usually the very first thing explained.
Where? I don't see a little double sided arrow
First, it looks like you are using AE on a very small monitor. Second, you have both the Switches and Modes columns visible because the second icon at the bottom left corner of the timeline is active. Third, it looks like you have some extra space between the last column and the layer view. You can close that up by hovering between the columns at the top of the timeline and waiting for the cursor to change and then dragging.
Please read up on the Timeline in the help files. Just type Timeline in the search help field at the top right corner of AE and go through some of the community assets that explain how to configure the timeline and work spaces. Also, make sure that your monitor complies with the minimum system requirements. I'm guessing that you are going to have problems with some of the other panels that are necessary when working with After Effects.
I apologize for my mistake. Those two panels cannot be drag resized in relationship to each other. But you can ()like Rick said) control the columns in the left side of the panel by dragging them. For example making the "Leyer Names" column a little smaller could save you some space. Also, in addition to toggling the "Toggle Switches and Modes" to get a little extra space, at the top of the columns where the names and icons are, if you right click there you get a drop down menu where you can show and hide columns. For example you could turn off the color swatches and "#" columns if you really desperate for space.