To simplify the expression, we need to find a common denominator for the fractions involved. The least common denominator (LCD) for 26, 64, and 32 is 64.

So, let's rewrite the expression with the LCD:

-4/9 x (1/26 - 32/64 + -4/32) = -4/9 x (1/26 - 32/64 + -4/32) x (64/64)

Now, we can simplify each fraction:

1/26 = 2/52
32/64 = 32/64
-4/32 = -2/16

Substituting these values back into the expression:

-4/9 x (2/52 - 32/64 - 2/16) x (64/64)

Now, let's simplify the expression inside the parentheses:

2/52 - 32/64 - 2/16 = 2/52 - 32/64 - 8/64
= 2/52 - 40/64
= 2/52 - 5/8

To subtract fractions, we need a common denominator. The LCD for 52 and 8 is 416.

So, let's rewrite the expression with the LCD:

2/52 - 5/8 = 2/52 - 5/8 x (52/52)
= 2/52 - 5/8 x (52/52)
= 2/52 - 260/416
= 2/52 - 65/104

Now, let's subtract the fractions:

2/52 - 65/104 = 1/26 - 65/104
= (1/26 x 4/4) - 65/104
= 4/104 - 65/104
= -61/104

Substituting this value back into the expression:

-4/9 x (-61/104) x (64/64)

Now, let's multiply the fractions:

-4/9 x (-61/104) = (4 x 61) / (9 x 104)
= 244/936

Substituting this value back into the expression:

244/936 x (64/64)

Finally, let's multiply the fractions:

244/936 x (64/64) = (244 x 64) / (936 x 64)
= 15616/59904

Therefore, the simplified expression is 15616/59904.