Browse at the string functions in the online docs . You need to extract one letter at a time. You could do:
<cfset string = "acthaychyaggdsdy">
<cfset word = "">
<cfset j = 1>
<cfset wordarray = arrayNew(1)>
<cfloop index="i" from="1" to="#len(string)#">
<cfset word = Insert(mid(string, i, 1), word, len(word))>
<cfif i mod 3 EQ 0>
<cfset wordarray[j] = word>
<cfset j = j + 1>
<cfset word = "">
</cfif>
</cfloop>
<cfoutput>
<br>
<cfloop index="i" from="1" to="#arraylen(wordarray)#">
#wordarray#<br>
</cfloop>
</cfoutput>
There is a bug in the code. It doesn't get the last character. I'll leave the fix up to you.