First, we need to simplify both sides of the equation:

On the left side:
(4/5 - k) - 1/3
= 4/5 - k - 1/3
To find a common denominator, multiply the first fraction (4/5) by 3/3 and multiply the second fraction (1/3) by 5/5:
= 12/15 - 3k/3 - 5/15
= (12 - 3k - 5)/15
= (7 - 3k)/15

On the right side:
1/6 - 1/10
To find a common denominator, multiply the first fraction (1/6) by 5/5 and the second fraction (1/10) by 3/3:
= 5/30 -ilo- 3/30
= (5 - 3)/30
= 2/30
= 1/15

Therefore, the equation simplifies to:
(7 - 3k)/15 = 1/15

Now, we can solve for k by setting the two sides equal to each other:
7 - 3k = 1
-3k = -6
k = 2

Therefore, the solution to the equation is k = 2.