Fortunately, you have a very small attribute list with just 4 attributes and 9 total levels. The number of choice tasks to ask each respondent is a common question. Usually, CBC practitioners choose between 8 and 14 choice tasks, which take a typical respondent somewhere around two to three minutes.
Most CBC practitioners want to estimate stable individual-level utilities using HB analysis. This leads to more accuracy and flexibility for market predictions and market segmentation than if you ask fewer choice tasks per respondent and are limited to aggregation techniques like aggregate logit.
A rule of thumb we teach in our trainings is that for reasonable HB estimation in CBC, you want each level to be shown to each respondent six or more times. With only 2 or 3 levels per each attribute, this is very easily attainable if you show three product concepts (alternatives) per task and show even as few as six choice tasks.
If your attribute levels have complex (long) text, then things may not be as easy as it appears for your study. So, you'll have to consider that.
Assuming your attribute levels are reasonably compact, given your small attribute list, I'd think 8 choice tasks each with 3 product concepts should be sufficient.