Hello,
you must always do update from Book it back-end (Check Updates)
Try to repair it by SQL query (replace #_ with your joomla db prefix):
ALTER TABLE `#__booking_subject` ADD `featured` TINYINT NOT NULL AFTER `state`
if it will throw similar error after sql update, continue with:
ALTER TABLE `#__booking_price` ADD `adult_occupancy_price` text NOT NULL
ALTER TABLE `#__booking_price` ADD `child_occupancy_price` text NOT NULL
ALTER TABLE `#__booking_reservation_items` ADD `adult_occupancy` int(11) NOT NULL DEFAULT \'0\'
ALTER TABLE `#__booking_reservation_items` ADD `child_occupancy` int(11) NOT NULL DEFAULT \'0\'
ALTER TABLE `#__booking_subject` ADD `max_adult_occupancy` int(11) NOT NULL DEFAULT \'0\'
ALTER TABLE `#__booking_subject` ADD `max_child_occupancy` int(11) NOT NULL DEFAULT \'0\'
ALTER TABLE `#__booking_reservation_type` ADD `dynamic_gap_time` tinyint(1) NOT NULL DEFAULT 0
ALTER TABLE `#__booking_price` ADD `deposit_type` TINYINT NOT NULL DEFAULT \'1\'
ALTER TABLE `#__booking_price` ADD `deposit_include_supplements` TINYINT NOT NULL DEFAULT \'0\'
ALTER TABLE `#__booking_price` ADD `time_range` TINYINT NOT NULL DEFAULT \'0\'
ALTER TABLE `#__booking_price` ADD `head_piece` INT NOT NULL, ADD `tail_piece` INT NOT NULL
INSERT INTO `#__booking_payment` (`id`, `title`, `alias`, `checked_out`, `checked_out_time`) VALUES
(10, 'Cash', 'cash', 0, '0000-00-00 00:00:00') ON DUPLICATE KEY UPDATE `id` = 10;
INSERT INTO `#__booking_payment` (`id`, `title`, `alias`, `checked_out`, `checked_out_time`) VALUES
(11, 'Cheque', 'cheque', 0, '0000-00-00 00:00:00') ON DUPLICATE KEY UPDATE `id` = 11;