The leasehold building improvement should be amortized over the lesser of the remaining life of the lease, which is 6 years, the life of the said improvement is 8 years. To get the amortization for a year, the calculation should be:
$48,000 / 6 = $8,000 (amortization for a year),
$8,000 / 12 * 6months( jan -june ) = $4,000
So with that, the amount of leasehold improvement would be like this:
$48,000 - $4,000 = $44, 000