If x+1 is a factor of $2x^3 + ax^2 + 2bx + 1$ then find the values of $a$ and $b$ given that $2a - 3b = 4$
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$$(x+1)\mid (2x^3+ax^2+2bx+1)\Longleftrightarrow 2(-1)^3+a(-1)^2+2b(-1)+1=0$$
So we get the following linear system in the unknowns $\,a,b\,$ :
Can you take it from here?