Hello,
You need to apply the font you loaded to the quote of the day area of the page using CSS:
There are different ways of applying CSS, below is one way, highlighted in bold text:
<link href="https://fonts.googleapis.com/css?family=Merriweather" rel="stylesheet">
<div style="font-family: 'Merriweather', serif;">
<script type="text/javascript" src="https://www.brainyquote.com/link/quotena.js"></script>
<small><a href="https://www.brainyquote.com/quotes/topics/topic_nature.html" target="_blank" rel="nofollow">more Nature Quotes</a></small>
</div>
This encloses the quote of the day in a HTML <div> tag and then applies the Merriweather font to its content.