To calculate the carrying value of the asset after two years, we'll use the reducing balance method, which is also known as the double-declining balance method. The formula for calculating the annual depreciation under this method is:

Annual Depreciation = Asset Cost × Depreciation Rate

First, we'll find the annual depreciation for the first year:

Year 1 Depreciation = €12,000 × 40% = €4,800

After the first year, the carrying value will be:

Carrying Value after Year 1 = Asset Cost - Year 1 Depreciation Carrying Value after Year 1 = €12,000 - €4,800 = €7,200

For the second year, we'll calculate the depreciation based on the new carrying value:

Year 2 Depreciation = Carrying Value after Year 1 × Depreciation Rate Year 2 Depreciation = €7,200 × 40% Year 2 Depreciation = €2,880

Finally, the carrying value after two years will be:

Carrying Value after Year 2 = Carrying Value after Year 1 - Year 2 Depreciation Carrying Value after Year 2 = €7,200 - €2,880 = €4,320

So, the carrying value of the asset after two years is €4,320.