Calculate tax for the 0% band.

The first £11,000 of earnings are not taxed.

$$\text{Tax}_1 = \pounds11,000 \times 0\% = \pounds0$$

This band applies to earnings in excess of £11,000 up to £43,000.
The amount in this band is $\pounds43,000 - \pounds11,000 = \pounds32,000$.

$$\text{Tax}_2 = \pounds32,000 \times 20\% = \pounds32,000 \times 0.20 = \pounds6,400$$

This band applies to earnings in excess of £43,000 up to £150,000.
Carys's total earnings are £45,600. The portion of her earnings that falls into this band is:

$$\pounds45,600 - \pounds43,000 = \pounds2,600$$ $$\text{Tax}_3 = \pounds2,600 \times 40\% = \pounds2,600 \times 0.40 = \pounds1,040$$

Carys's earnings (£45,600) do not exceed £150,000, so no tax is paid in this band.

$$\text{Tax}_4 = \pounds0$$

Add the tax from each band:

$$\text{Total Tax} = \text{Tax}_1 + \text{Tax}_2 + \text{Tax}_3 + \text{Tax}_4$$ $$\text{Total Tax} = \pounds0 + \pounds6,400 + \pounds1,040 + \pounds0 = \pounds7,440$$

Carys paid a total of £7,440 in tax.

The final answer is $\pounds7,440$.