You are trying to solve 8 equations for 6 variables, but they are not consistent for all 8 equations.
syms a b c d e x
equ1 = a + b == (0.83/12);
equ2 = c == (0.036/2);
equ3 = (0.048/16) + 2*0.21*x == 2*a + b + c + 2*d;
equ4 = 0.79*x == e;
equ5 = (a/(a + b + d + e)) == 0.109;
equ6 = (b/(b + a + d + e)) == 0.010;
equ7 = (d/(d + a + b + e)) == 0.071;
equ8 = (e/(e + a + b + d)) == 0.810;
sol = solve([equ1,equ2,equ3,equ4,equ5,equ6],[a,b,c,d,e,x]);
subs(equ7, sol), vpa(ans)
subs(equ8, sol), vpa(ans)
