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Factoring by grouping.

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Factoring by grouping: 8ax-2a+4bx-b
 
Group the terms as follows:
 
(8ax-2a)+(4bx-b)
 
Factor 2a out of the first two terms and b out of the second two terms
 
2a(4x-1) + b(4x-1)
 
Now factor (4x-1) out of both terms to get the fully factored expression
 
(2a+b)(4x-1)
 
Check:
 
(2a+b)(4x-1) = 8ax-2a+4xb-b
 
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You could also choose another grouping,  Instead of
 
(8ax-2a)+(4bx-b)
 
Group the terms as follows:
 
(8ax+4bx) - (2a+b)
 
Factor 4x out of the first terms
 
4x(2a+b) - (2a+b)
 
Now factor out (2a+b)
 
(2a+b)(4x-1)  --> same answer as before