\documentclass[a4paper,12pt, twoside]{article}
\usepackage{enumerate}
\renewcommand{\baselinestretch}{1.5}
\usepackage{amsmath, amsthm, amsfonts, mathrsfs, latexsym, amssymb,
pstricks,graphicx,setspace,textcomp}
\usepackage{pdfpages,caption}
\usepackage[round]{natbib}
\bibliographystyle{apa}
\usepackage{cite}
\usepackage{nomencl}
\usepackage{graphicx}
\usepackage{float}
\usepackage{underlin}
\usepackage{url}
\usepackage{longtable}
\usepackage{titletoc}
\usepackage{titlesec}
\usepackage[normalem]{ulem}
\usepackage{hyperref}
\usepackage{caption}
\usepackage{parskip}
\setlength{\parindent}{20pt}
\usepackage{setspace}
\usepackage{lipsum}
\usepackage{pdflscape}
\usepackage{multirow}
\usepackage[utf8x]{inputenc}
\begin document
\begin{landscape}
\chapter*{Plan of work}
\begin{tabular}{|c|*7{p{32mm}|}}
\hline
\multirow{2}{*}{Task} & \multicolumn{6}{c|}{Duration}\\
\cline{2-7}
& Jan-15 to May-15 & June-15 to Dec-15 & Jan-16 to May-16 & June-16 to Dec-16 & Jan-17 to May-17 & June-17 to Dec-17\\
\hline
\multirow{2}{*}{Course Work} & & &&&&\\
\cline{2-7}
& & &&&&\\
\hline
\multirow{2}{*}{Literature Survey} &&&&&&\\
\cline{2-7}
&&&&&&\\
\hline
\multirow{2}{*}{Develop CZM } &&&&&&\\
\cline{2-7}
&&&&&&\\
\hline
\multirow{2}{*}{Fracture Toughness} &&&&&&\\
\cline{2-7}
for pure modes &&&&&&\\
\hline
\multirow{2}{*}{Applying to mixed } &&&&&&\\
\cline{2-7}
mode cases &&&&&&\\
\hline
\multirow{2}{*}{Publications and } &&&&&&\\
\cline{2-7}
Thesis Preparation &&&&&&\\
\hline
\end{tabular}
\newpage
\end{landscape}
\end document
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Salim Bou
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user104426
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2That's a whole lot of unnecessary packages you're loading. For future reference, please read how to create a minimal example. – Werner Apr 29 '16 at 17:16
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1Related: https://tex.stackexchange.com/questions/156162/strike-out-a-table-cell – Henri Menke Apr 29 '16 at 20:55
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1You are also loading packages multiple times, packages you don't need (with 99.9999999999999999% probability) and packages in the wrong order. Expect things to break in strange ways. – cfr Apr 30 '16 at 02:49