Solution:

44x - 9 strings

4x4 - 9 strings

x44 - 9 strings

Total: 27 strings

I get that.

But what is wrong with this line of reasoning? I have two 4s with me. I have 3 positions for the first one and 2 for the second one. Then I will have a blank space that can be filled by one of 9 digits. So, the total number of strings is 3*2*9=54.