How To Create New Vertex or Segment When Extrude Passing or Intersection Other Object or Shape I am creating a computer table , To make the partition board (where the keyboard is kept). I added in two loop cuts on either leg and extruded the face formed by the loop cut as shown:

It is known that it can't make new vertex, edges, and faces when the extruded face passing through it. In short it can't merge with the middle leg.

In the left leg it has 3 face for each direction,  but the middle leg (since it don't have any loop cuts) still have only 1 face for each direction.(See the image)

Of course, the face or vertices count doesn't matter for the viewers of the final render...But for basic concept or fundamental, I think it's wrong??
So I hope you can help me to doing it right and clean.
Can you please point out what should I do. (if direct extrude is not recommended)
Any help is appreciated.
Thank you in advance.
The easiest way to do it is by Bridging the Edge Loops.

Make two legs for the table:



Create two edge loops on both the legs by Ctrl+R. Make sure that it's perfectly aligned or else you will get a slope. To place the loopcuts perfectly hold down Ctrl while sliding the edge loop. Which will get you this:



Now select the faces as shown and press F3 and type in Bridge edge loops.




There you have it.