Step 1: Define toss positions

First six tosses:
$T_1,T_2,T_3,T_4,T_5,T_6$

Last five tosses:
$T_4,T_5,T_6,T_7,T_8$

Notice overlap: $T_4,T_5,T_6$

Step 2: Conditions given

• Exactly 4 heads in first 6 tosses
• Exactly 3 heads in last 5 tosses

Let number of heads among overlapping tosses $T_4,T_5,T_6$ be $k$.

Then:

Heads in $(T_1,T_2,T_3)$ = $4-k$

Heads in $(T_7,T_8)$ = $3-k$

Possible values of $k$:

$k=1,2,3$

Step 3: Count favorable outcomes

Case 1: $k=1$

Choose 1 head among overlap:
$\binom{3}{1}$

Need $3$ heads among first three tosses:
$\binom{3}{3}$

Need $2$ heads among last two tosses:
$\binom{2}{2}$

Total:
$3 \times 1 \times 1 = 3$

Case 2: $k=2$

$\binom{3}{2}\binom{3}{2}\binom{2}{1}$

$= 3 \times 3 \times 2 = 18$

Case 3: $k=3$

$\binom{3}{3}\binom{3}{1}\binom{2}{0}$

$= 1 \times 3 \times 1 = 3$

Step 4: Total favorable outcomes

$3 + 18 + 3 = 24$

Total outcomes for 8 tosses:

$2^8 = 256$

So,

$ p = \frac{24}{256} = \frac{3}{32}$

Step 5: Compute $96p$

$96p = 96 \times \frac{3}{32}$

$= 3 \times 3 = 9$

Final Answer:

$\boxed{9}$