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Understanding the calculation of taxable income is essential for anyone navigating through tax laws. In our scenario with Laxmi's income, we first determine her total earnings, which amounts to Rs 22500. However, each individual may have a certain portion of their income that is not subject to tax, known as tax-free income. This could be due to various deductions, exemptions or a basic threshold under tax laws.

For Laxmi, Rs 7000 of her total income falls into this category. To calculate her taxable income, we simply subtract this tax-free amount from her total income:
\\( Taxable\_income = Total\_income - Tax\_free\_income \)
\\( Taxable\_income = 22500 - 7000 \)
This subtraction gives us Laxmi's income that is eligible for taxation. Understanding this fundamental step is crucial as it lays the foundation for further calculations related to income tax.

Once the taxable income is computed, the next key concept is the application of the income tax rate. In Laxmi's case, the income tax rate is given as 8%. This represents the percentage of the taxable income that will be paid as income tax.

To calculate the tax owed, apply the tax rate to the taxable income, which we already figured out in the previous step:
\\( Income\_tax = Taxable\_income \times Tax\_rate \)
\\( Income\_tax = (22500 - 7000) \times 0.08 \)
Performing this multiplication gives us the income tax Laxmi will need to pay. It's important to note that different incomes may be taxed at varying rates, depending on tax brackets or specific legislation. For simplicity, our exercise involves a flat tax rate.

After calculating the income tax, it's time to find out the net income, which is what the individual actually takes home. Net income is the remaining amount after the income tax amount has been deducted from the total income.

Laxmi's net income can be determined by:
\\( Net\_income = Total\_income - Income\_tax \)
\\( Net\_income = 22500 - ((22500 - 7000) \times 0.08) \)
This calculation shows the actual earning after fulfilling tax obligations. For individuals, understanding net income is vital as it represents the actual disposable income that can be used for savings, expenses, or investment. In Laxmi’s case, somewhat surprisingly, the calculated net income does not match any of the provided options exactly, indicating a possible miscalculation or rounding in the options presented. However, this conclusion highlights the need for meticulous attention to detail in income tax calculations.