Is basic solution an electrode?
"how will you make a cell from one electrode?".


There is no need to, because there is nothing which prohibits you from writing a Nernst equation for a half cell.* Remember the rule no.1 in electrochemistry, whenever you mention half-cell potential, your next automatic question should be "with respect to what?". If the textbook is quiet and you are required to look up tables, it is understood that it is with reference to the hydrogen electrode under standard condition which is set at 0 V (exactly).

Now at pH 10, your standard conditions have changed and the activity or hydrogen ion concentration differs. It is no longer zero. So proceed with the Nernst equation for the half cell and work it out.



*(Yes, there is no single electrode galvanic cell, but for fun and general knowledge, people have done single electrode reduction using electrostatics (Bard and others). Faraday did it centuries ago. It was published in a very reputable magazine.)