VBA Formula

North_Yorks 
I'm not sure I understand what you mean by " added the End With that I was missing". Perhaps you are missing that instead of 

Sheets("Americas").Activate

I'm using 

With Sheets("Americas")

and where you have something like 

Rows("8:18").EntireRow.Hidden = True

I have added a period to the front so it is now:

.Rows("8:18").EntireRow.Hidden = True

I'm using an entirely different approach that happens to look very similar. You are trying to activate the sheet and hoping that the rows will reference the active sheet. I'm explicitly telling Excel to link the rows to the specific worksheet and I'm not activating each sheet to do it. By not activating each worksheet, your first activate remains the active worksheet.

Without the WITH statement the new code would look like this (which may make things clearer),

Sheets("Americas").Rows("8:18").EntireRow.Hidden = True
Sheets("Americas").Rows("21:30").EntireRow.Hidden = True
Sheets("Americas").Rows("33:42").EntireRow.Hidden = True
Sheets("Americas").Rows("45:49").EntireRow.Hidden = True

Sheets("ANZASAF").Rows("8:18").EntireRow.Hidden = True
Sheets("ANZASAF").Rows("21:24").EntireRow.Hidden = True
Sheets("ANZASAF").Rows("27:36").EntireRow.Hidden = True
Sheets("ANZASAF").Rows("39:45").EntireRow.Hidden = True

The WITH statement allows us to not duplicate the Sheets("sheet name") on every row.