Are we suggesting that there are four independent variables here with values A, B, C, and so forth, the same four variables every time, or there are more than four variables, and in any given scenario we only use only four of them?
If we have four independent variables, and if those variables are more or less independent of each other, and if the relationship is really more or less linear, a linear regression may work, keeping in mind all the limits and assumptions of a linear regression. This is a "multiple linear regression" with four explanatory variables.
If on the other hand we have some model which is taking four variables in one scenario and another four variables in another scenario, is that because in the thing being modeled the unused variables are not applicable, or are the unused variables there but unknown? Probably it's not going to be a good place to use a linear regression, but it depends on what is going on with the actual thing being modeled and why you would have different variables in different scenarios. Are they still there in the thing being modeled, you just don't have access to them? Or are they not applicable?
So for example, if the "A" above is for number of apples, "B" for number of blueberries, "C" for number of currants, "D" for dates, "F" for figs, "G" for guavas, "H" for honeydew, and "Y" is the size of your fruit salad, is the first row only taking into account apples, blueberries, currants, and dates because the other fruit are all unused? If so, then the variables really are there, set to zero, and you could make a nice linear regression using eight variables for those fruit, though with any given salad you used only four and left the others as zero. Only the four ingredients are applicable, but the others are really all accounted for, being zero. You really have all eight variables every time, likely they are independent of each other, and likely the relationship to the size of the fruit salad is linear, so a multiple linear regression may work well.