Here are some options:

\documentclass{article}
\usepackage{amsmath,eqparbox}
\begin{document}
\[
\boxed{
\begin{aligned}
3\mathrm{d}6 + \text{ability} + \text{skill} & \ge 10 + \text{ability} + \text{skill} \\
&\text{or} \\
3\mathrm{d}6 + \text{ability} + \text{skill} & \ge 10 + \text{ability} + 4 \\
&\text{or} \\
3\mathrm{d}6 + \text{ability} + 4 & \ge 10 + \text{ability} + \text{skill} \\
&\text{or} \\
3\mathrm{d}6 + \text{ability} + 4 & \ge 10 + \text{ability} + 4
\end{aligned}
}
\]
\begin{gather*}
\boxed{\eqmakebox[LHS][r]{$3\mathrm{d}6 + \text{ability} + \text{skill}$}
\eqmakebox[RHS][l]{${}\geq 10 + \text{ability} + \text{skill}$}} \\
\text{or} \\
\boxed{\eqmakebox[LHS][r]{$3\mathrm{d}6 + \text{ability} + \text{skill}$}
\eqmakebox[RHS][l]{${}\geq 10 + \text{ability} + 4$}} \\
\text{or} \\
\boxed{\eqmakebox[LHS][r]{$3\mathrm{d}6 + \text{ability} + 4$}
\eqmakebox[RHS][l]{${}\geq 10 + \text{ability} + \text{skill}$}} \\
\text{or} \\
\boxed{\eqmakebox[LHS][r]{$3\mathrm{d}6 + \text{ability} + 4$}
\eqmakebox[RHS][l]{${}\geq 10 + \text{ability} + 4$}}
\end{gather*}
\newlength{\LHSlong}\newlength{\LHSshort}%
\newlength{\RHSlong}\newlength{\RHSshort}%
\newcommand{\LHSfill}{\hspace*{\dimexpr\LHSlong-\LHSshort}}%
\newcommand{\RHSfill}{\hspace*{\dimexpr\RHSlong-\RHSshort}}%
\settowidth{\LHSlong}{$3\mathrm{d}6 + \text{ability} + \text{skill}$}%
\settowidth{\RHSlong}{${}\geq 10 + \text{ability} + \text{skill}$}%
\settowidth{\LHSshort}{$3\mathrm{d}6 + \text{ability} + 4$}%
\settowidth{\RHSshort}{${}\geq 10 + \text{ability} + 4$}%
\begin{gather*}
\boxed{3\mathrm{d}6 + \text{ability} + \text{skill} \geq 10 + \text{ability} + \text{skill}} \\
\text{or} \\
\boxed{3\mathrm{d}6 + \text{ability} + \text{skill} \geq 10 + \text{ability} + 4} \RHSfill \\
\text{or} \\
\LHSfill\boxed{3\mathrm{d}6 + \text{ability} + 4 \geq 10 + \text{ability} + \text{skill}} \\
\text{or} \\
\LHSfill\boxed{3\mathrm{d}6 + \text{ability} + 4 \geq 10 + \text{ability} + 4}\RHSfill
\end{gather*}
\end{document}
The last option relies on the fact that your constructions seems deterministic with two fixed L
eft/R
ight H
and S
ides. As such, we're able to measure their widths and use it to correct for the too-short equation sides.