How to connect an L293D and an MPU6050 to run together?
There a some mistakes with the wiring of the supply voltage (Vss) according to the datasheet (http://www.ti.com/lit/ds/symlink/l293.pdf) of the L293D a those on pin 8 (Vss2) and 16 (Vss1). I think those are not connected because each Vss is for one motor of the driver. So you have to connect 9V (or 12V) to both pins.
There is also something wrong with the capacitor (polarity). And your connection of the battery to the breadboard is a bit weird because + of the battery is usally the red not the black wire / marked row on the breadboard.