You seem to be assuming a leap from an LDR sensing system to a L293D H-brudge IC circuit (plus an H-Bridge) without any mention of some manner of digitizing (or PWM) circuit(s) in between.
As such, either you haven't completely thought out your system requirements or you are unaware of of the component "blocks" needed to achieve your goal (a line following robot) using the components you have, thus far, listed.
Please list what you currently have as parts for this line following robot and those you think you'll need.
And, while not terribly sophisticated, your initial circuit could do the job. The robot would "wig-wag" its way around the course defined by the lines (slowing it somewhat, for sure) but it would follow the line.
Also:
Why do you think you need 4 LDRs? You only need 2: 1 to detect the left side of the line and the other to detect the right side.
You could, in fact, get away with just one detector, but that would require a considerably more sophisticated controller system for the motors.