1. Given reactions and heats released

$\mathrm{C}(s)+\mathrm{O}_2(g)\rightarrow \mathrm{CO}_2(g)+400\,\text{kJ}$

So, formation of $1$ mole of $\mathrm{CO}_2$ from carbon releases $400\,\text{kJ}$.

$\mathrm{C}(s)+\frac12\mathrm{O}_2(g)\rightarrow \mathrm{CO}(g)+100\,\text{kJ}$

So, formation of $1$ mole of $\mathrm{CO}$ from carbon releases $100\,\text{kJ}$.

2. Mass of pure carbon in coal

Coal purity $=60\%$.

Given coal burnt $=0.6\,\text{kg}=600\,\text{g}$.

Therefore, mass of pure carbon:

$600\times \frac{60}{100}=360\,\text{g}$

3. Moles of carbon present

Molar mass of carbon $=12\,\text{g mol}^{-1}$.

$n_C=\frac{360}{12}=30\,\text{mol}$

4. Distribution of carbon into CO and CO$_2$

$60\%$ of carbon forms CO:

$30\times \frac{60}{100}=18\,\text{mol}$

Remaining $40\%$ forms CO$_2$:

$30\times \frac{40}{100}=12\,\text{mol}$

5. Heat released

From $18$ mol CO:

$18\times 100=1800\,\text{kJ}$

From $12$ mol CO$_2$:

$12\times 400=4800\,\text{kJ}$

Total heat generated:

$1800+4800=6600\,\text{kJ}$

6. Correct option

$\boxed{6600\,\text{kJ}}$

So, the correct option is D.

7. Comparison with stored answer

Stored correct answer: D

Derived answer: D

They match.