#### Answer

66351

#### Work Step by Step

Let's first find the total number of strings of four lowercase letters
There are 26 letters in the alphabet.
So, number of choices: 4
no. of options: 26
therefore the number of words = $26\times26\times26\times26=26^4$
Now, let's find the number of strings of four lowercase letters which $do$ $not$ have $x$ in them. As if the alphabet didn't have $x$ in it.
So, number of choices: 4
no. of options: 25 (all the letters except $x$)
therefore the number of words without any $x$ = $25\times25\times25\times25=25^4$
therefore the number of words with at least one $x$ = the total number of words - the number of words without any $x$
=$26^4 - 25^4$
=456976 - 390625
=66351