The number of four -digit numbers strictly grater than $4321$ that can be formed using the digits $0,1,2,3,4,5$ (repetition of digits is allowed) is:

(1) The number of four-digit numbers Strating with 5 is equal to $6^3 = 216$

(2) Starting with 44 and 55 is equal to $36\times 2 = 72$

(3) Starting with 433, 434 and 435 is equal to $6\times 3 = 18$

(4) Remaining numbers are 4322, 4323, 4324, 4325 is equal to 4

so total number are

$716 + 72 + 18 + 4 = 310$