Abcd are the points on the circle such that angle acb 40 and angle dab 60 find the angle dba

Check the picture below.

notice the left-side, that's the inscribed angle theorem, as you'd already know.

now, notice the right-side, the inscribed angle at vertex C, is intercepting the arc at AB, however, the angle at vertex D, is also intercepting the arc AB, what the heck does that mean?

well, it means the angle at D, is the same as the angle at C, thus ∡D is 40°.

and then the triangle ADB has then two angles, a 60° one and a 40° one, the angle at B, namely ∡DBA is 180 - 60 - 40.