What about the other possible situations—2, 3, 4 or 5 boxes checked?
You specified that there were "4 on the left, 2 on the right." Does that arrangement have any bearing on the results?
My assumptions below are that the result cell should contain 0 if no boxes are checked, and should contain 1 if any of the boxes are checked.
For the example, it's assumed the boxes are in columns B, C, D, E, G and H of ROW 2, and that cell F2—the cell for which "4 are on the left and two on the right"—will never contain the boolean values 'true' or 'false'

The formula shown below the table is in cell O2. Filled down, it is incremented by Numbers to natch the Bn:Hn references to its current row.
The bottom four rows of the table are to test the effects of a variety of values containing 'true' in column F. This column is included in the range of cells to be counted, but will count as a 0 provided the cell does not contain the boolean value true.
IN cell F7, the letters TRUE were entered in the cell. On pressing return, this text was interpreted as a Boolean, and was counted.
F8: the keystrokes here were ' T R U E (without the spaces). Note the apostrophe preceding the text. This is a signal to Numbers that everything that follows is TEXT. The apostrophe itself is not displayed.
In F8, the enclosing letters around "true" establish that this is a text string, not a Boolean value.
In F9, the cell has been formatted as Text (before the entry was made, preventing Numbers from converting it to a Boolean value.
I also tested entering a number in column F, and found it had no effect on the count.
Here is a text version of the formula. MIN(COUNTIF(B2:H2,TRUE),1)
Regards,
Barry