Help with moderation analysis in SPSS for creativity research

I'm trying to test out some moderating variables on my data. I ran an experiment looking at metaphor and creativity, with 3 moderating conditions.
I have a massive spreadsheet with 6 conditions: 1 control (no image), 1 neutral (a fish), one experimental (a lightbulb), and the experimental is split into 4 sub groups (color realistic, b&w realistic, color cartoony, b&w cartoony). Additionally, there is another moderating variable (familiarity and perceived aptness of metaphor).
Dependent variable was the number of solutions to a RAT task conducted, independent variable is the group, moderating variables are color/b&w, cartoon/real, familiarty, aptness.

Do I run a regression on this data? dependent variable is continuous, but the rest are categorical, so i'm not sure that would work. Also, using SPSS.

I've done plenty of moderation regression analyses before, but for some reason I can't get my head around the correct way to analyze this data. Designed the experiment just fine with my advisor, but the stats is stumping me at the moment. Any help would be greatly appreciated. Thanks!