Prerequisite
Bit rate is a specific case of baud rate.
Baud rate means the rate at which symbols(or elements or characters) get sent across a channel.
$\text{Baud rate} = \text{Number of symbols being sent per unit time} / \text{Size of a symbol}$
Very clearly, baud rate is nothing but the transfer rate.
When we say bit rate, we mean that 1 symbol = 1 bit.
Now, coming to the question
The bit rate given in the question is 1200 bits/second.
We have to get the data transfer rates.
For serial transmission, as per the question, Size of a character = $12\ bits$.
Baud rate/Transfer rate = $\frac{1200\ bits/sec}{1 \ character}$
=> $\frac{1200\ bits/sec}{12 \ bits}=100\ characters/sec$
For synchronous transmission, as per the question, Size of 30 characters = $30(8)+3(8)$.
Hence, size of a character = $8.8\ bits$
Baud rate/Transfer rate = $\frac{1200\ bits/sec}{1 \ character}$
=> $\frac{1200\ bits/sec}{8.8 \ bits}\approx136\ characters/sec$
Option C