Great question and a nice start to a story. You might use either, depending on what you (as the writer / observer) have in mind. The first use should be plural because you're referring to more than one possible problem (corn, chicken, and yams) and also because you used the word "any," which is used with plurals. The second use should be singular if you have in mind one specific problem he could have had but didn't. "... but had a problem with ..." It should be plural if you have in mind more than one potential problem OR if you are referring to the same problem repeated many times. "...but had problems with..." A few other edits: My son tried to put some food into a deep, hot cooking pot**. He didn't have any problems with the corn, chicken, or yams, but had problems with the eggs. He couldn't help but drop them and they all ended up broken. Some of these edits are grammatical corrections and others are to reflect colloquialisms. I would recommend a couple of classes with a teacher to review some of your writing together. This can help you learn to edit more of your writing yourself. ** Here's a link to a helpful article that outlines order in which we use adjectives: https://dictionary.cambridge.org/us/grammar/british-grammar/adjectives-order

For number 1, where the number of problems is zero, it can be correct either way, depending on whether you were expecting one problem or multiple problems that never materialized. For number 2, it depends on whether he actually had one problem or multiple problems.

You shoud use ur second example but add an "s" to tge first problem: He didn't have any problems with corn, chickens, and yams, but had a problem with eggs.

Problem