Scheudle K-1

If your Schedule K-1 has capital gains, the amount will be reported on Schedule D.

K-1s have boxes for net short-term and net long-term capital gains. Those amounts will transfer to Schedule D lines 5 and 12.

I do see Long Term gain but then I see in line 10 a positive dollar amount, line 12,  a negative dollar amount, and in line 13 a capital gain distribution  (positive) amount.  This is the part I do not understand.  Is the LTCG rate the same and with any investment based on income level?

The amount on line 13 is unlikely to have come from the K-1.  Check for a 1099-DIV with an amount in box 2a. 

Otherwise, review the K-1 and your K-1 entries  to see where the Capital gains distribution amount came from.