The problem asks for the maximum line utilization efficiency and throughput for a statistical time-division multiplexer (TDM) setup.

Step 1: Identify Given Parameters

• Number of terminals, $N = 16$.
• Terminal port speed, $R_{term} = 1200 \text{ bps}$.
• Line port speed, $C = 9600 \text{ bps}$.
• Multiplexing method: Statistical TDM using bit-map.
• Data Link Protocol: HDLC.
• Provided Efficiency, $E = 0.696$.

Step 2: Calculate Maximum Throughput

The throughput ($T$) is the actual rate of data transmitted over the line. It is calculated by multiplying the line capacity by the line utilization efficiency.

Formula: $T = E \times C$

Substituting the given values:

$T = 0.696 \times 9600 \text{ bps}$

$T = 6678.4 \text{ bps}$

Step 3: Interpret the Results

The maximum line utilization efficiency is given as 0.696. This value represents the fraction of the total line capacity ($9600 \text{ bps}$) that is effectively used for data transmission. This efficiency accounts for the statistical multiplexing gain (allowing total potential input greater than line capacity) and the overhead introduced by the HDLC protocol.

The maximum throughput, calculated in Step 2, is approximately 6678 bps (rounding $6678.4 \text{ bps}$). This is the effective data rate achieved on the $9600 \text{ bps}$ line under the specified conditions.