Let's break down the expression step by step. The expression you provided is:

[
(4.3 + 2.8) (4.3 - 2.8) + 4.488 \frac{(3.6 - 0.63)}{(4.61 + 7.27)} * 0.12
]

Calculate the first part:
[
(4.3 + 2.8) = 7.1
]
[
(4.3 - 2.8) = 1.5
]
Now multiply these results:
[
7.1 * 1.5 = 10.65
]

Calculate the second part:
[
3.6 - 0.63 = 3.6 - 0.63 = 2.97
]
[
4.61 + 7.27 = 11.88
]
Now divide:
[
\frac{2.97}{11.88} \approx 0.249
]
Finally, multiply by 4.488 and 0.12:
[
4.488 0.249 0.12 \approx 0.133
]

Combine the two parts:
[
10.65 + 0.133 \approx 10.783
]

Thus, the final result of the expression is approximately:

[
\boxed{10.783}
]