Synchronous communication requires that the clocks in the transmitting and receiving devices are synchronized – running at the same rate – so the receiver can sample the signal at the same time intervals used by the transmitter. No start or stop bits are required. For this reason “synchronous communication permits more information to be passed over a circuit per unit time.
2400 baud means that the serial port is capable of transferring a maximum of 2400 bits per second.
Number of 8-bit characters that can be transmitted per second = 2400/8 = 300

Given bandwidth is 2400 bps
Each character consists of (7+1)bits = 8 bits
Synchronous transmission is a data transfer method which is characterized by a continuous stream of data in the form of signals which are accompanied by regular timing signals which are generated by some external clocking mechanism meant to ensure that both the sender and receiver are synchronized with each other.
Once sender and receiver synchronized means no need to use start and stop bits every time
Total number of characters can be transmitted per second is =bandwidth/ number of bits in each character=2400/8 = 300