VBA Code To Populate A Cell Automatically Whenever Another Cell Is Filled In Manually?

I have a spreadsheet with 6 hidden columns (B to G). Rows 1 to 14 are frozen and have data that comes from another work book and these rows will be protected. The user will enter data from H14 to U14 and then H15 to U15 for the next row and so on down the sheet. The number of rows of data over a week is variable, a minimum of 21 rows (3 per day) but no maximum.

When the user starts entering new data in the column range H to U I would like to automatically populate the 6 hidden cells on that row with information from particular cells in protected rows 1 to 14. For example B14 would populate with the value from I4, C14 would populate with the value from I5, D14 from I6, E14 from I7 and so on whenever someone enters a value anywhere from H14 through to U14.

I can understand that a worksheet change event would be useful to do this but I guess then it wouldn't want to run every time each cell is populated so I think if it had to activate on a single cell change then the cell in column L would be best. Also, as I understand it, there can be only one block of code per sheet that operates on a worksheet change event, have I got that right? If that is the case then I assume all the code to populate the hidden cells on each row will need to be in this block of code.