\documentclass[12pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage[all]{xy}
\usepackage{amsmath,amsthm,amssymb,color,latexsym}
\usepackage{geometry}        
\geometry{letterpaper}    
\usepackage{graphicx}
\usepackage[shortlabels]{enumitem}
\usepackage{MnSymbol,wasysym}
\newtheorem{problem}{Problem}
\newenvironment{solution}[1][\it{Solution}]{\textbf{#1. } }{$\smiley$}
\newcommand{\HH}{\mathbb{H}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\Z}{\mathbb{Z}}
\renewcommand\qedsymbol{$\smiley$}
\newcommand{\C}{\mathbb{C}}
\usepackage{xcolor}
\begin{document}
\noindent \textbf{Laura Kurtz} \hfill Homework \#12\\
Algebra II/Math 7211



\hrulefill
\begin{problem}
    Problem environment. Here you can state the problem that was given to you. 
\end{problem}
\begin{solution}
    This is a solution environment. Should be used for computations. Key words: Find, solve.
\end{solution}
\begin{problem}
    here is another problem
\end{problem}
\begin{proof}
    Here is a proof environment. Should be used when you're proving things. Key words: Prove, show.
\end{proof}

Note: If you want a regular box to end your proofs instead of the smiley face, you can delete the renew command qed symbol in the header.
\end{document}