We are given a sequence where:
- The first term $\(\left(a_1\right)$ is $\mathbf{4 .}\)$
- The second term $\(\left(a_2\right)\)$ is 8 .
- For all $\(n>2\)$, the $n$-th term is obtained by subtracting the term before the previous term from the previous term:

$$
\(a_n=a_{n-1}-a_{n-2}\)
$$


We need to find the sum of the first $\mathbf{1 0 0}$ terms of this sequence.

Step 1: Generate the Sequence
Let's compute the first few terms to identify any patterns:
1. Given:

$$
\(a_1=4, \quad a_2=8\)
$$

2. Compute Subsequent Terms:

$$
\(\begin{gathered}
a_3=a_2-a_1=8-4=4 \\
a_4=a_3-a_2=4-8=-4 \\
a_5=a_4-a_3=-4-4=-8 \\
a_6=a_5-a_4=-8-(-4)=-4 \\
a_7=a_6-a_5=-4-(-8)=4 \\
a_8=a_7-a_6=4-(-4)=8
\end{gathered}\)
$$

3. Observed Pattern:

The sequence repeats every 6 terms:

$$
\(4,8,4,-4,-8,-4,4,8,4,-4,-8,-4, \ldots\)
$$



3. Observed Pattern:

The sequence repeats every 6 terms:

$$
\(4,8,4,-4,-8,-4,4,8,4,-4,-8,-4, \ldots\)
$$


Step 2: Determine the Sum of One Full Cycle (6 Terms)
Compute the sum of the first 6 terms:

$$
\(S_6=4+8+4+(-4)+(-8)+(-4)=0\)
$$


Key Insight: The sum of every $\(\mathbf{6}\)$-term block is $\(\mathbf{0}\)$.

Step 3: Compute the Number of Complete Cycles in 100 Terms
1. Total Terms: 100
2. Terms per Cycle: 6
3. Number of Complete Cycles:

$$
\(\text { Number of cycles }=\left\lfloor\frac{100}{6}\right\rfloor=16 \quad(\text { since } 16 \times 6=96)\)
$$

4. Remaining Terms: $100-96=4$

Step 4: Calculate the Sum of the First $\mathbf{1 0 0}$ Terms
1. Sum of $\(\mathbf{1 6}\)$ Complete Cycles:

$$
\(16 \times S_6=16 \times 0=0\)
$$

2. Sum of the Remaining 4 Terms:

The 97th to 100th terms correspond to the first 4 terms of the sequence:

$$
\(\begin{gathered}
a_{97}=a_1=4, \quad a_{98}=a_2=8, \quad a_{99}=a_3=4, \quad a_{100}=a_4=-4 \\
S_{\text {remaining }}=4+8+4+(-4)=12
\end{gathered}\)
$$


3. Total Sum:

$$
\(S_{100}=0+12=12\)
$$


Final Answer
The sum of the first 100 terms of the sequence is:
\(12\)