A frame $F_b$ is being translated with a speed $v$ according to another frame $F_a$.
A point $A$ is attached to $F_a$. $B$ is attached to $F_b$.
$D_a$ is the distance $AB$ viewed from $Fa$ and $D_b$ is the distance $AB$ viewed from $F_b$.
What is the relation between $D_a$ and $D_b$ (in special relativity)?
(Is there something like $D_a=+vt_a$ and $D_b=-vt_b$?)
I would guess you are thinking about deriving the Lorentz contraction, but if so this isn't the way to go about it.
Suppose we put the point $A$ at the origin of $F_a$ and the point $B$ at the origin of $F_b$, and for convenience we take the zero time to be when the two origins coincide i.e. $A$ and $B$ are at the same point.
An observer at the origin in $F_a$ sees $B$ moving with velocity $+v$, so the distance to point $B$ is:
$$ D_a = vt $$
An observer at the origin in $F_b$ sees $A$ moving with velocity $-v$, so the distance to point $A$ is:
$$ D_b = -vt $$
So for both observers the distance between the points is the same.
If you're interested in deriving the Lorentz contraction see my answer to How do I derive the Lorentz contraction from the invariant interval?.
