The sumifs function will exclude it.
=SUMIFS($F$12:$R$12,$F$12:$R$12,">"&0,$F$11:$R$11,1)
-the texts with red color is the sum range.
-the texts with blue color is the criteria range and criteria which excludes negative values.
-the texts with orange color is the criteria range and criteria which only includes the important columns.
Another alternative but lengthy formula will be using if statements:
=SUM(IF(F12>0,F12,0),IF(H12>0,H12,0),IF(J12>0,J12,0),IF(L12>0,L12,0),IF(N12>0,N12,0),IF(P12>0,P12,0),IF(R12>0,R12,0))