Given:
The values a, b, c, l, and m are in arithmetic progression (AP).

To Find:
The value of a - 4b + 6c - 4l + m.

Solution:
Step 1: Determine the common difference of the arithmetic progression (AP).
The common difference (d) represents the constant difference between any two consecutive terms in the AP. We can find the common difference using any three terms from the AP.

Step 2: Express all the terms in terms of the first term (a) and the common difference (d).
The terms in the AP can be written as:
a, a + d, a + 2d, a + 3d, a + 4d, ...

Step 3: Substitute the expressions for the terms in the given expression.
a - 4b + 6c - 4l + m
= (a + 0d) - 4(a + 1d) + 6(a + 2d) - 4(a + 3d) + (a + 4d)
= a - 4a + 6a - 4a + a + 0d - 4d + 12d - 12d + 4d
= (a - 4a + 6a - 4a + a) + (0d - 4d + 12d - 12d + 4d)
= 4a + 0d
= 4a

Step 4: Simplify the expression.
Since the value of a - 4b + 6c - 4l + m simplifies to 4a, we can conclude that the value of a - 4b + 6c - 4l + m is equal to 4a.

Therefore, the value of a - 4b + 6c - 4l + m is 4a.