I'm taking a guess here.....I'm assuming you want the Count of cells for year 2013, since you are using COUNTIF....
If Columns B and C Only contains a Number representing the Year you're trying to Count, then use formula in E34,
<colgroup><col><col><col><col><col></colgroup><thead>
</thead><tbody>
[TD="align: center"]34[/TD]
[TD="align: right"]2013[/TD]
[TD="align: right"]2015[/TD]
[TD="align: right"][/TD]
[TD="align: right"]5[/TD]
[TD="align: center"]35[/TD]
[TD="align: right"]2014[/TD]
[TD="align: right"]2016[/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: center"]36[/TD]
[TD="align: right"]2015[/TD]
[TD="align: right"]2013[/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: center"]37[/TD]
[TD="align: right"]2013[/TD]
[TD="align: right"]2018[/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: center"]38[/TD]
[TD="align: right"]2013[/TD]
[TD="align: right"]2014[/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: center"]39[/TD]
[TD="align: right"]2017[/TD]
[TD="align: right"]2013[/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: center"]40[/TD]
[TD="align: right"]2018[/TD]
[TD="align: right"]2017[/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: center"]41[/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: center"]42[/TD]
[TD="align: right"]1/5/2013[/TD]
[TD="align: right"]9/8/2015[/TD]
[TD="align: right"][/TD]
[TD="align: right"]5[/TD]
[TD="align: center"]43[/TD]
[TD="align: right"]3/4/2014[/TD]
[TD="align: right"]5/6/2016[/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: center"]44[/TD]
[TD="align: right"]4/5/2015[/TD]
[TD="align: right"]4/27/2013[/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: center"]45[/TD]
[TD="align: right"]6/6/2013[/TD]
[TD="align: right"]9/9/2018[/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: center"]46[/TD]
[TD="align: right"]5/4/2013[/TD]
[TD="align: right"]7/7/2014[/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: center"]47[/TD]
[TD="align: right"]5/7/2017[/TD]
[TD="align: right"]3/19/2013[/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: center"]48[/TD]
[TD="align: right"]12/12/2018[/TD]
[TD="align: right"]4/20/2017[/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
</tbody>
<thead>[TR="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=DAE7F5]#DAE7F5[/URL] "]
[TH="width: 10, bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=DAE7F5]#DAE7F5[/URL] "]E34[/TH]
[TH="width: 10, bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=DAE7F5]#DAE7F5[/URL] "]E42[/TH]
Let us know if this is not what you're trying to do, and please explain in detail.
Edit: seems you posted an explanation of what you want while I was posting this, I'm sure someone will get back to you.