You can add and subtract any like terms. Since 8w, -4w, and 4w are all like terms, since 8, -4, and 4 all tell how many w's you have. This is the essentially same as saying "There are 8 apples, subtract 4 apples, and add 4 apples." (Don't forget that 8w-4w is the same as 8w + -4w). To solve, just add 8, subtract 4, and add 4. Leave w alone. The answer is 4w.
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2x-3x+1 can be simplified (by combining like terms, or terms with the same number/type of variables) to -x+1. This is not an equation, but an "expression," meaning that there is no equals sign, and you cannot solve for x without an equals sign. If, for instance, that entire expression was equal to 7, -x+1=7 -x = 6 x = -6
That equals x.
It means to rewrite the expression so that it is in its simplest form. You can do this by combining like terms. For example: The equation 2x + 3x = 5 can be simplified to 5x = 5 by combining the "x's".
10x and 6y are terms of an algebraic expression
It combines like terms and results in the least amount if variables to solve for