I do not know how familiar you are with basic algebra, so I will do it step by step. Please feel free to hurry the process!
$1$. Subtract $d$ from both sides. You should get
$$Y-d=(0.5a)\text{erf}\left(\frac{x-b}{c\sqrt{2}}+ 0.5\right)$$
$2$. Divide both sides by $0.5a$. You should get
$$\frac{Y-d}{0.5a}=\text{erf}\left(\frac{x-b}{c\sqrt{2}}+ 0.5\right)$$
Now for brevity let
$$w=\frac{Y-d}{0.5a}$$
So we have
$$w=\text{erf}\left(\frac{x-b}{c\sqrt{2}}+ 0.5\right)$$
$3$. Now apply $\text{erfinv}$ to both sides. This is where we use the fact that $\text{erfinv}(\text{erf}(u))=u$. We get
$$\text{erfinv}(w)= \left(\frac{x-b}{c\sqrt{2}}+ 0.5\right)$$
$4$. Subtract $0.5$ from both sides. We get
$$\text{erfinv}(w)-0.5= \left(\frac{x-b}{c\sqrt{2}}\right)$$
$5$. Multiply both sides by $c\sqrt{2}$. We get
$$c\sqrt{2}(\text{erfinv}(w)-0.5)= {x-b}$$
$6$. Finally, add $b$ to both sides, and because I like $x$ on the left of the $=$ sign, interchange the two sides. We get
$$x= c\sqrt{2}(\text{erfinv}(w)-0.5) +b$$