If 0 isn't a valid result, you could code the SKIPIF field along the lines of:
{SKIPIF {MERGEFIELD Boy4}= 0}
or:
{SKIPIF «Boy4»= 0}

Otherwise, you would probably need to code the SKIPIF field along the lines of:
{SKIPIF {MERGEFIELD Boy4}<> {={MERGEFIELD Boy4}}}
or:


{SKIPIF «Boy4}<> {=«Boy4»}}

Note: The field brace pairs (i.e. '{ }') for the above example are all created in the document itself, via Ctrl-F9 (Cmd-F9 on a Mac); you can't simply type them or copy & paste them from this message. Nor is it practicable to add them via any of the standard Word dialogues. Likewise, you can't type or copy & paste the chevrons (i.e. '« »') - they're part of the actual mergefields, which you can insert from the mailmerge toolbar. The spaces represented in the field construction are all required.

__________________
Cheers,
Paul Edstein
[Fmr MS MVP - Word]

Many thanks.

I'm close now (especially thanks to your tip about the spaces being vital).

The fields are now invisible if null but there is still a carriage return when the field is null (or zero).

The code I've got is:

Maybe I need to take the carriage returns out of the document and into the fields somehow.

A ha!

It seems I just need to put a carriage return in the code:
Thank you again for your help!