Can you manipulate a function?

Put $1-x$ in place of $x$ :

$f(x)+2 f(1-x)=3 (1-x)$

Multiply by 2 in the given equation:

$2 f(1-x) + 4 f(x)=6 x$

Substract :

$3 f(x)=9 x-3 \\ f(x)=3 x-1$

So, $f(0)=-1$

f(1 - x) + 2 f(x) = 3x

For x = 0 we get: f(1) + 2 f(0) = 0 (i)

For x = 1 we get: f(0) + 2 f(1) = 3 (ii)

By (partially) solving the simultaneous equations ( 2(i) - (ii) ):

3f(0) = - 3

$f(0) = \boxed {- 1}$