[SalesForce] How to create a validation rule based on two picklist values and two multi-picklist fields

Try this as the condition

ISPICKVAL(OnBoarding_Setup__c, 'New Account')) &&
(
    ISPICKVAL(Office_Type__c, 'Blank') ||
    ISPICKVAL(Office_Type__c, 'Not Selected') || 
    /* Add more values here if needed, join them with "||" ("logical OR") */
    ISPICKVAL(Office_Type__c, '')
)

Although I admit I'm not sure if your picklist really has the values like "Blank"...

EDIT 1 If you want to allow any value of choice1, choice3, or choice5 but do not want to allow choice2, choice4, or choice6 then you should create rule like this

 if(Family__c == 'X', 
        if( 
            OR(
                INCLUDES(choices__c,'choice2'), 
                INCLUDES(choices__c,'choice4'),
                INCLUDES(choices__c,'choice6')
            ), 
            True, 
            False
        ),
        False
    )

You can use formula something like bellow:

if(Family__c == 'X', 
    if(TEXT(choices__c) == 'choice1; choice3; choice5', 0, 1),0)

So basically the idea is to check the value of Family__c.

If value of Family__c Is X Then check additional condition else return false.

The additional condition should check if Text value of choices__c is 'choice1; choice3; choice5' then it should return false or else true.

When validation rule returns true it shows error to user and stop the processing.