A single checkbox can be looked at as being boolean it is either checked or it isn't.
in psuedocode it would be checkbox.checked
A textbox group changes this, so that now you look at the value assigned to each individual checkbox and is that checkbox value checked yes or no
psuedocode here would be checkbox.value.checked
in the database you can save this information as either a string or a yes/no value for each checkbox. If they are Yes/No you can simply write a WHERE clause for each of the checkboxes that looks to see if the value is checked (true) or Not checked(false)
That should point you in the right direction.