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If you've watched my video on eighth notes and gotten the hang of them, then sixteenth notes shouldn't be too bad. With eighth notes, you count two notes for every click of a metronome. For sixteenth notes, you double that number to four. You can count the four notes that make up a beat like this, 'One ee and a Two ee and a Three ee and a...' and so on.
Sixteenth notes are played really fast even at moderate tempos, and it might take you some practice to get to the point that you can play them with even volume and duration, but they are an important part of learning to play the piano so the time is worth it.
Next, you can practice counting 16th note triplets.