The value of the annuity after the last investment is $141,920.
You are looking for the future value of an annuity.
Future value of annuity = Annuity x Future value interest factor of annuity
Because this annuity is compounded semi-annually, you need to convert the figures to a semi-annual basis:
Number of periods = 6 years x 2 = 12 semi annual periods
Interest = 6% / 2 = 3% per semi annum
Future value of annuity = Annuity x Future value interest factor of annuity 3%, 12 periods
= 10,000 x 14.1920
= $141,920
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