Calculation to show 0 when 0 is entered otherwise will be blank when SPECIFIC fields are empty.

This condition is not necessary:

If B and C is 0 (zero), then D will display 0 (zero)

If either of those fields is zero then the result of multiplying them by any other value will be zero, no matter what.

In the custom calculation script for D, you could do something like:

// Custom calculate script
(function () {

    // Get the input field values, as strings
    var sA = getField("A").valueAsString;
    var sB = getField("B").valueAsString;
    var sC = getField("C").valueAsString;

    if (sB && sC) {  // If both of these input fields are not empty...

        // If both of these field values are zero when converted to a number...
        if (+sB === 0 && +sC === 0) {
            event.value = 0;  // Set this field value to zero
            return;
        } else {
            event.value = sA * sB * sC;  // Set this field value to this product
            return;
    }

    } else {
        // Blank this field since B and C inputs are blank
        event.value = "";
        return;
    }

})();

You'd have to change the field names in the getField statements to the actual field names. Be sure to set the field calculation order to what makes sense.