To solve this expression, we need to follow the order of operations (PEMDAS/BODMAS):

Step 1: Calculate the exponents.
4⁶ = 4 * 4 * 4 * 4 * 4 * 4 = 4,096
9⁵ = 9 * 9 * 9 * 9 * 9 = 59,049
6⁹ = 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 = 531,441
(-8)⁴ = (-8) * (-8) * (-8) * (-8) = 4,096
3¹³ = 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 = 1,594,323

Step 2: Perform the multiplication and division from left to right.
4,096 * 59,049 = 242,221,504
531,441 * 240 = 127,626,240
127,626,240 / 4,096 = 31,104
31,104 * 1,594,323 = 49,605,013,792

Step 3: Perform the addition and subtraction from left to right.
49,605,013,792 + (2 * 6¹¹)
= 49,605,013,792 + (2 * 362,797,056)
= 49,605,013,792 + 725,594,112
= 50,330,607,904

Therefore, the value of the expression 4⁶ × 9⁵ - 6⁹ × 240 / -8⁴ × 3¹³ + 2 × 6¹¹ is 50,330,607,904.