Two light sources emit light at the same moment but in opposite directions. At what speed the distance between two light fronts is increasing? c or c * 2?
Note, that there is only one coordinate system here - a system, where these two light sources are placed and they don't move.
I think you are asking: If I turn on a lightbulb, I can imagine a sphere of light spreading radially outward from the bulb at the speed of light. How fast is the diameter of the sphere increasing in the lightbulb's frame? The answer is 2*c.
Two light sources emit light at the same moment but in opposite directions.
For the question under consideration it is suitable (and also in accordance to the answer already submitted by mcFreid) to specify only one source ("light bulb $L$") having stated a particular signal ($L_{\mathscr E \ast}$, e.g. "the light bulb turning on");
and let's also consider additional participants ($A$, $B$ ... on the one hand, and $P$, $Q$ ... on the other) which are all at rest wrt. $L$ and (pairwise) wrt. each other, where their distance ratios wrt. $L$ satisfy
$\frac{AL}{AP} + \frac{LP}{AP} = 1, \, \frac{AL}{AQ} + \frac{LQ}{AQ} = 1, \, \frac{BL}{BP} + \frac{LP}{BP} = 1$ and so on
(as a specific setup implementation of $P$, $Q$, etc. having been "in opposite direction from $L$" wrt. $A$, $B$, ...).
Finally, set distance ratios $AL / PL = 1$, $BL / QL = 1$, and so on.
Correspondingly, $A$ and $P$ observed the signal event $\mathscr E \! \ast$ simultaneously, $B$ and $Q$ observed the signal event $\mathscr E \! \ast$ simultaneously, and so on.
At what speed the distance between two light fronts is increasing?
I believe that "distance between two light fronts [propagating] in opposite directions" is supposed to mean more correctly the "distance between participants (located in opposite directions from $L$) who observed signal event $\mathscr E \! \ast$ simultaneously".
The values of those distances (as a function of $L$'s duration "$\tau_L( X )$" from having stated $L_{\mathscr E \ast}$ until indication $L_{\circledS}^{X \circledR \mathscr E \ast}$ of $L$ simultaneous to $X$'s indication of having received the signal $\mathscr E \! \ast$) are
$AP = AL + LP = 2 AL = 2 \, c \, \tau_L( A )$,
$BQ = BL + LQ = 2 BL = 2 \, c \, \tau_L( B )$,
and so on.
However: the quantity $2 \, c$ is some "speed" only in a rather lose sense, similar to "phase speed".
It is obviously the quotient of "some distance" divided by "some duration", but not speed (such as: the speed of the signal having been transmitted) in the strict sense of the quotient
