Paste Values to the End of a Range Column Without Extending Past the Range Column

I'm using columns D4-AY4 as a range of cells for my data. For each cell, the values are just single words with a space and number appended to it, like so: Word 1, Word 10, Word 2, Word 20.
Any cell within that range will either be blank or as described above.

I'm trying to figure out how to move all the words within this range that have a 0 (actual zero), to then move those words to the end of the range, which is column AY4, BUT it can't extend past AY4.

So, this means it needs to calculate how many cells from the end of the range (AY4) so that it can assign the correct column to begin pasting the words so that they do not extend beyond the AY4 column.

Any suggestions using VBA to do this?

Mike